LMFDB - Embedded newform 117.8.q.b.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,8,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$117 = 3^{2} \cdot 13$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	117.q (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$36.5490479816$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368$ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{10}\cdot 3^{7}\cdot 13^{4}$
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.6
Root			$16.7213i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.8.q.b.82.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.4811 - 8.36065i) q^{2} +(75.8010 - 131.291i) q^{4} -94.5127i q^{5} +(1225.76 + 707.691i) q^{7} -394.655i q^{8} +(-790.187 - 1368.64i) q^{10} +(-1241.02 + 716.501i) q^{11} +(5632.23 - 5570.14i) q^{13} +23667.0 q^{14} +(6402.95 + 11090.2i) q^{16} +(1394.31 - 2415.02i) q^{17} +(24883.0 + 14366.2i) q^{19} +(-12408.7 - 7164.15i) q^{20} +(-11980.8 + 20751.4i) q^{22} +(25299.9 + 43820.7i) q^{23} +69192.4 q^{25} +(34990.7 - 127751. i) q^{26} +(185827. - 107287. i) q^{28} +(-114179. - 197763. i) q^{29} -154870. i q^{31} +(229191. + 132324. i) q^{32} -46629.4i q^{34} +(66885.8 - 115850. i) q^{35} +(-63637.4 + 36741.1i) q^{37} +480443. q^{38} -37299.9 q^{40} +(-593980. + 342934. i) q^{41} +(393865. - 682194. i) q^{43} +217246. i q^{44} +(732739. + 423047. i) q^{46} -690181. i q^{47} +(589882. + 1.02171e6i) q^{49} +(1.00198e6 - 578493. i) q^{50} +(-304382. - 1.16168e6i) q^{52} +1.69205e6 q^{53} +(67718.5 + 117292. i) q^{55} +(279294. - 483752. i) q^{56} +(-3.30686e6 - 1.90922e6i) q^{58} +(427536. + 246838. i) q^{59} +(-1.10386e6 + 1.91195e6i) q^{61} +(-1.29481e6 - 2.24268e6i) q^{62} +2.78609e6 q^{64} +(-526449. - 532317. i) q^{65} +(-1.95500e6 + 1.12872e6i) q^{67} +(-211380. - 366121. i) q^{68} -2.23683e6i q^{70} +(-349495. - 201781. i) q^{71} -509572. i q^{73} +(-614359. + 1.06410e6i) q^{74} +(3.77231e6 - 2.17795e6i) q^{76} -2.02825e6 q^{77} -1.91796e6 q^{79} +(1.04817e6 - 605160. i) q^{80} +(-5.73431e6 + 9.93212e6i) q^{82} +4.57733e6i q^{83} +(-228250. - 131780. i) q^{85} -1.31719e7i q^{86} +(282771. + 489774. i) q^{88} +(-3.05403e6 + 1.76324e6i) q^{89} +(1.08457e7 - 2.84176e6i) q^{91} +7.67102e6 q^{92} +(-5.77037e6 - 9.99457e6i) q^{94} +(1.35779e6 - 2.35176e6i) q^{95} +(4.21540e6 + 2.43376e6i) q^{97} +(1.70843e7 + 9.86360e6i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$14 q + 3 q^{2} + 383 q^{4} - 2772 q^{7} - 509 q^{10} - 6516 q^{11} + 5109 q^{13} + 47916 q^{14} - 633 q^{16} + 38403 q^{17} + 43254 q^{19} - 89409 q^{20} - 125882 q^{22} + 68550 q^{23} + 39380 q^{25} - 361959 q^{26}+ \cdots - 16173003 q^{98}+O(q^{100})$ 14 * q + 3 * q^2 + 383 * q^4 - 2772 * q^7 - 509 * q^10 - 6516 * q^11 + 5109 * q^13 + 47916 * q^14 - 633 * q^16 + 38403 * q^17 + 43254 * q^19 - 89409 * q^20 - 125882 * q^22 + 68550 * q^23 + 39380 * q^25 - 361959 * q^26 - 234780 * q^28 - 221583 * q^29 + 878067 * q^32 - 659616 * q^35 - 565347 * q^37 - 953640 * q^38 - 77182 * q^40 - 1716057 * q^41 - 882692 * q^43 - 3267480 * q^46 + 2653979 * q^49 - 145128 * q^50 + 4962178 * q^52 + 1791210 * q^53 + 2453536 * q^55 + 7457952 * q^56 - 14978127 * q^58 + 1189032 * q^59 + 3858525 * q^61 - 1904142 * q^62 + 14570922 * q^64 - 10424661 * q^65 + 4674330 * q^67 - 9569619 * q^68 + 25203126 * q^71 - 8640105 * q^74 + 12934506 * q^76 - 19599336 * q^77 - 30688440 * q^79 - 29127963 * q^80 - 37359719 * q^82 - 22436313 * q^85 + 27045536 * q^88 - 2123160 * q^89 + 37205532 * q^91 + 47685588 * q^92 + 19138810 * q^94 + 43420386 * q^95 - 68556288 * q^97 - 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$ .

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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

)

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

$2$	14.4811	−	8.36065i	1.27996	−	0.738984i	0.303118	−	0.952953i	$-0.401972\pi$
$2$	14.4811	−	8.36065i	1.27996	−	0.738984i	0.976840	+	0.213969i	$0.0686392\pi$
$3$		0			0
$3$		0			0
$4$	75.8010	−	131.291i	0.592195	−	1.02571i
$5$		−	94.5127i		−	0.338139i	−0.985604	−	0.169069i	$-0.945924\pi$
$5$		−	94.5127i		−	0.338139i	0.985604	−	0.169069i	$-0.0540762\pi$
$6$		0			0
$7$	1225.76	+	707.691i	1.35071	+	0.779831i	0.988349	−	0.152207i	$-0.0486381\pi$
$7$	1225.76	+	707.691i	1.35071	+	0.779831i	0.362359	+	0.932039i	$0.381971\pi$
$8$		−	394.655i		−	0.272523i
$9$		0			0
$10$	−790.187	−	1368.64i	−0.249879	−	0.432803i
$11$	−1241.02	+	716.501i	−0.281127	+	0.162309i	−0.633934	−	0.773387i	$-0.718561\pi$
$11$	−1241.02	+	716.501i	−0.281127	+	0.162309i	0.352806	+	0.935696i	$0.385227\pi$
$12$		0			0
$13$	5632.23	−	5570.14i	0.711015	−	0.703177i
$13$	5632.23	−	5570.14i	0.711015	−	0.703177i
$14$	23667.0			2.30513
$15$		0			0
$16$	6402.95	+	11090.2i	0.390805	+	0.676894i
$17$	1394.31	−	2415.02i	0.0688316	−	0.119220i	−0.829556	−	0.558424i	$-0.811406\pi$
$17$	1394.31	−	2415.02i	0.0688316	−	0.119220i	0.898387	+	0.439204i	$0.144740\pi$
$18$		0			0
$19$	24883.0	+	14366.2i	0.832272	+	0.480512i	0.854630	−	0.519238i	$-0.173784\pi$
$19$	24883.0	+	14366.2i	0.832272	+	0.480512i	−0.0223580	+	0.999750i	$0.507117\pi$
$20$	−12408.7	−	7164.15i	−0.346833	−	0.200244i
$21$		0			0
$22$	−11980.8	+	20751.4i	−0.239888	+	0.415497i
$23$	25299.9	+	43820.7i	0.433582	+	0.750986i	0.997179	−	0.0750644i	$-0.0239162\pi$
$23$	25299.9	+	43820.7i	0.433582	+	0.750986i	−0.563597	+	0.826050i	$0.690583\pi$
$24$		0			0
$25$	69192.4			0.885662
$26$	34990.7	−	127751.i	0.390433	−	1.42547i
$27$		0			0
$28$	185827.	−	107287.i	1.59976	−	0.923625i
$29$	−114179.	−	197763.i	−0.869344	−	1.50575i	−0.862668	−	0.505771i	$-0.831208\pi$
$29$	−114179.	−	197763.i	−0.869344	−	1.50575i	−0.00667640	−	0.999978i	$-0.502125\pi$
$30$		0			0
$31$		−	154870.i		−	0.933686i	−0.884340	−	0.466843i	$-0.845391\pi$
$31$		−	154870.i		−	0.933686i	0.884340	−	0.466843i	$-0.154609\pi$
$32$	229191.	+	132324.i	1.23644	+	0.713859i
$33$		0			0
$34$		−	46629.4i		−	0.203462i
$35$	66885.8	−	115850.i	0.263691	−	0.456727i
$36$		0			0
$37$	−63637.4	+	36741.1i	−0.206541	+	0.119247i	−0.599703	−	0.800223i	$-0.704715\pi$
$37$	−63637.4	+	36741.1i	−0.206541	+	0.119247i	0.393162	+	0.919469i	$0.371381\pi$
$38$	480443.			1.42036
$39$		0			0
$40$	−37299.9			−0.0921506
$41$	−593980.	+	342934.i	−1.34595	+	0.777083i	−0.987673	−	0.156533i	$-0.949968\pi$
$41$	−593980.	+	342934.i	−1.34595	+	0.777083i	−0.358275	+	0.933616i	$0.616635\pi$
$42$		0			0
$43$	393865.	−	682194.i	0.755454	−	1.30848i	−0.189695	−	0.981843i	$-0.560750\pi$
$43$	393865.	−	682194.i	0.755454	−	1.30848i	0.945148	−	0.326641i	$-0.105917\pi$
$44$			217246.i			0.384474i
$45$		0			0
$46$	732739.	+	423047.i	1.10993	+	0.640820i
$47$		−	690181.i		−	0.969663i	−0.874608	−	0.484831i	$-0.838881\pi$
$47$		−	690181.i		−	0.969663i	0.874608	−	0.484831i	$-0.161119\pi$
$48$		0			0
$49$	589882.	+	1.02171e6i	0.716274	+	1.24062i
$50$	1.00198e6	−	578493.i	1.13361	−	0.654490i
$51$		0			0
$52$	−304382.	−	1.16168e6i	−0.300197	−	1.14571i
$53$	1.69205e6			1.56116			0.780579	−	0.625057i	$-0.214924\pi$
$53$	1.69205e6			1.56116			0.780579	+	0.625057i	$0.214924\pi$
$54$		0			0
$55$	67718.5	+	117292.i	0.0548830	+	0.0950601i
$56$	279294.	−	483752.i	0.212522	−	0.368099i
$57$		0			0
$58$	−3.30686e6	−	1.90922e6i	−2.22545	−	1.28486i
$59$	427536.	+	246838.i	0.271013	+	0.156470i	0.629348	−	0.777124i	$-0.283322\pi$
$59$	427536.	+	246838.i	0.271013	+	0.156470i	−0.358335	+	0.933593i	$0.616655\pi$
$60$		0			0
$61$	−1.10386e6	+	1.91195e6i	−0.622674	+	1.07850i	0.366312	+	0.930492i	$0.380620\pi$
$61$	−1.10386e6	+	1.91195e6i	−0.622674	+	1.07850i	−0.988986	+	0.148011i	$0.952713\pi$
$62$	−1.29481e6	−	2.24268e6i	−0.689979	−	1.19508i
$63$		0			0
$64$	2.78609e6			1.32851
$65$	−526449.	−	532317.i	−0.237771	−	0.240422i
$66$		0			0
$67$	−1.95500e6	+	1.12872e6i	−0.794118	+	0.458484i	−0.841410	−	0.540397i	$-0.818274\pi$
$67$	−1.95500e6	+	1.12872e6i	−0.794118	+	0.458484i	0.0472923	+	0.998881i	$0.484941\pi$
$68$	−211380.	−	366121.i	−0.0815235	−	0.141203i
$69$		0			0
$70$		−	2.23683e6i		−	0.779455i
$71$	−349495.	−	201781.i	−0.115888	−	0.0669077i	0.440936	−	0.897539i	$-0.354647\pi$
$71$	−349495.	−	201781.i	−0.115888	−	0.0669077i	−0.556823	+	0.830631i	$0.687980\pi$
$72$		0			0
$73$		−	509572.i		−	0.153312i	−0.997058	−	0.0766558i	$-0.975576\pi$
$73$		−	509572.i		−	0.153312i	0.997058	−	0.0766558i	$-0.0244243\pi$
$74$	−614359.	+	1.06410e6i	−0.176243	+	0.305261i
$75$		0			0
$76$	3.77231e6	−	2.17795e6i	0.985735	−	0.569114i
$77$	−2.02825e6			−0.506295
$78$		0			0
$79$	−1.91796e6			−0.437668			−0.218834	−	0.975762i	$-0.570225\pi$
$79$	−1.91796e6			−0.437668			−0.218834	+	0.975762i	$0.570225\pi$
$80$	1.04817e6	−	605160.i	0.228884	−	0.132146i
$81$		0			0
$82$	−5.73431e6	+	9.93212e6i	−1.14850	+	1.98927i
$83$			4.57733e6i			0.878697i	0.898317	+	0.439348i	$0.144791\pi$
$83$			4.57733e6i			0.878697i	−0.898317	+	0.439348i	$0.855209\pi$
$84$		0			0
$85$	−228250.	−	131780.i	−0.0403129	−	0.0232746i
$86$		−	1.31719e7i		−	2.23307i
$87$		0			0
$88$	282771.	+	489774.i	0.0442329	+	0.0766137i
$89$	−3.05403e6	+	1.76324e6i	−0.459206	+	0.265123i	−0.711710	−	0.702473i	$-0.752079\pi$
$89$	−3.05403e6	+	1.76324e6i	−0.459206	+	0.265123i	0.252504	+	0.967596i	$0.418746\pi$
$90$		0			0
$91$	1.08457e7	−	2.84176e6i	1.50873	−	0.395315i
$92$	7.67102e6			1.02706
$93$		0			0
$94$	−5.77037e6	−	9.99457e6i	−0.716565	−	1.24113i
$95$	1.35779e6	−	2.35176e6i	0.162480	−	0.281423i
$96$		0			0
$97$	4.21540e6	+	2.43376e6i	0.468962	+	0.270755i	0.715805	−	0.698300i	$-0.246060\pi$
$97$	4.21540e6	+	2.43376e6i	0.468962	+	0.270755i	−0.246843	+	0.969055i	$0.579393\pi$
$98$	1.70843e7	+	9.86360e6i	1.83360	+	1.05863i
$99$		0			0
$100$	5.24485e6	−	9.08434e6i	0.524485	−	0.908434i
$101$	−698709.	−	1.21020e6i	−0.0674795	−	0.116878i	0.830312	−	0.557299i	$-0.188162\pi$
$101$	−698709.	−	1.21020e6i	−0.0674795	−	0.116878i	−0.897791	+	0.440421i	$0.854829\pi$
$102$		0			0
$103$	−6.54055e6			−0.589772			−0.294886	−	0.955533i	$-0.595282\pi$
$103$	−6.54055e6			−0.589772			−0.294886	+	0.955533i	$0.595282\pi$
$104$	−2.19829e6	−	2.22279e6i	−0.191632	−	0.193768i
$105$		0			0
$106$	2.45027e7	−	1.41466e7i	1.99822	−	1.15367i
$107$	3.30316e6	+	5.72123e6i	0.260667	+	0.451488i	0.966419	−	0.256970i	$-0.0827243\pi$
$107$	3.30316e6	+	5.72123e6i	0.260667	+	0.451488i	−0.705752	+	0.708459i	$0.749391\pi$
$108$		0			0
$109$			1.24329e7i			0.919561i	0.888033	+	0.459781i	$0.152072\pi$
$109$			1.24329e7i			0.919561i	−0.888033	+	0.459781i	$0.847928\pi$
$110$	1.96127e6	+	1.13234e6i	0.140496	+	0.0811153i
$111$		0			0
$112$			1.81252e7i			1.21905i
$113$	−5.94659e6	+	1.02998e7i	−0.387698	+	0.671513i	−0.992140	−	0.125137i	$-0.960063\pi$
$113$	−5.94659e6	+	1.02998e7i	−0.387698	+	0.671513i	0.604441	+	0.796650i	$0.293396\pi$
$114$		0			0
$115$	4.14161e6	−	2.39116e6i	0.253937	−	0.146611i
$116$	−3.46194e7			−2.05929
$117$		0			0
$118$	8.25491e6			0.462514
$119$	3.41817e6	−	1.97348e6i	0.185943	−	0.107354i
$120$		0			0
$121$	−8.71684e6	+	1.50980e7i	−0.447312	+	0.774766i
$122$			3.69161e7i			1.84059i
$123$		0			0
$124$	−2.03330e7	−	1.17393e7i	−0.957693	−	0.552924i
$125$		−	1.39234e7i		−	0.637616i
$126$		0			0
$127$	−1.58001e7	−	2.73665e7i	−0.684457	−	1.18551i	−0.973607	−	0.228230i	$-0.926706\pi$
$127$	−1.58001e7	−	2.73665e7i	−0.684457	−	1.18551i	0.289150	−	0.957284i	$-0.406627\pi$
$128$	1.10091e7	−	6.35611e6i	0.463999	−	0.267890i
$129$		0			0
$130$	−1.20741e7	−	3.30707e6i	−0.482005	−	0.132020i
$131$	1.45168e7			0.564184			0.282092	−	0.959387i	$-0.408972\pi$
$131$	1.45168e7			0.564184			0.282092	+	0.959387i	$0.408972\pi$
$132$		0			0
$133$	2.03337e7	+	3.52190e7i	0.749437	+	1.29806i
$134$	−1.88737e7	+	3.26901e7i	−0.677625	+	1.17368i
$135$		0			0
$136$	−953099.	−	550272.i	−0.0324902	−	0.0187582i
$137$	−4.58302e7	−	2.64601e7i	−1.52276	−	0.879163i	−0.999638	−	0.0269023i	$-0.991436\pi$
$137$	−4.58302e7	−	2.64601e7i	−1.52276	−	0.879163i	−0.523117	−	0.852261i	$-0.675231\pi$
$138$		0			0
$139$	−2.74729e7	+	4.75844e7i	−0.867666	+	1.50284i	−0.00329010	+	0.999995i	$0.501047\pi$
$139$	−2.74729e7	+	4.75844e7i	−0.867666	+	1.50284i	−0.864376	+	0.502847i	$0.832286\pi$
$140$	−1.01400e7	−	1.75630e7i	−0.312313	−	0.540943i
$141$		0			0
$142$	−6.74808e6			−0.197775
$143$	−2.99868e6	+	1.09481e7i	−0.0857539	+	0.313086i
$144$		0			0
$145$	−1.86911e7	+	1.07913e7i	−0.509152	+	0.293959i
$146$	−4.26035e6	−	7.37914e6i	−0.113295	−	0.196232i
$147$		0			0
$148$			1.11400e7i			0.282469i
$149$	−3.93097e7	−	2.26955e7i	−0.973527	−	0.562066i	−0.0732176	−	0.997316i	$-0.523327\pi$
$149$	−3.93097e7	−	2.26955e7i	−0.973527	−	0.562066i	−0.900310	+	0.435250i	$0.856660\pi$
$150$		0			0
$151$		−	3.65804e7i		−	0.864627i	−0.901723	−	0.432313i	$-0.857697\pi$
$151$		−	3.65804e7i		−	0.864627i	0.901723	−	0.432313i	$-0.142303\pi$
$152$	5.66970e6	−	9.82021e6i	0.130951	−	0.226813i
$153$		0			0
$154$	−2.93712e7	+	1.69575e7i	−0.648036	+	0.374144i
$155$	−1.46372e7			−0.315716
$156$		0			0
$157$	−6.28265e7			−1.29567			−0.647835	−	0.761781i	$-0.724325\pi$
$157$	−6.28265e7			−1.29567			−0.647835	+	0.761781i	$0.724325\pi$
$158$	−2.77741e7	+	1.60354e7i	−0.560197	+	0.323430i
$159$		0			0
$160$	1.25063e7	−	2.16615e7i	0.241383	−	0.418088i
$161$			7.16180e7i			1.35248i
$162$		0			0
$163$	2.44610e7	+	1.41225e7i	0.442402	+	0.255421i	0.704616	−	0.709589i	$-0.251119\pi$
$163$	2.44610e7	+	1.41225e7i	0.442402	+	0.255421i	−0.262214	+	0.965010i	$0.584453\pi$
$164$			1.03979e8i			1.84074i
$165$		0			0
$166$	3.82695e7	+	6.62847e7i	0.649343	+	1.12470i
$167$	7.42098e7	−	4.28450e7i	1.23297	−	0.711857i	0.265324	−	0.964159i	$-0.414521\pi$
$167$	7.42098e7	−	4.28450e7i	1.23297	−	0.711857i	0.967649	+	0.252302i	$0.0811877\pi$
$168$		0			0
$169$	695541.	−	6.27447e7i	0.0110846	−	0.999939i
$170$	−4.40707e6			−0.0687984
$171$		0			0
$172$	−5.97107e7	−	1.03422e8i	−0.894752	−	1.54976i
$173$	5.36018e6	−	9.28411e6i	0.0787079	−	0.136326i	−0.823985	−	0.566612i	$-0.808254\pi$
$173$	5.36018e6	−	9.28411e6i	0.0787079	−	0.136326i	0.902693	+	0.430286i	$0.141587\pi$
$174$		0			0
$175$	8.48130e7	+	4.89668e7i	1.19627	+	0.690667i
$176$	−1.58923e7	−	9.17544e6i	−0.219732	−	0.126862i
$177$		0			0
$178$	−2.94837e7	+	5.10673e7i	−0.391843	+	0.678692i
$179$	5.73747e7	+	9.93759e7i	0.747713	+	1.29508i	0.948916	+	0.315528i	$0.102181\pi$
$179$	5.73747e7	+	9.93759e7i	0.747713	+	1.29508i	−0.201203	+	0.979549i	$0.564485\pi$
$180$		0			0
$181$	−7.50660e7			−0.940953			−0.470477	−	0.882412i	$-0.655918\pi$
$181$	−7.50660e7			−0.940953			−0.470477	+	0.882412i	$0.655918\pi$
$182$	1.33298e8	−	1.31829e8i	1.63898	−	1.62092i
$183$		0			0
$184$	1.72941e7	−	9.98473e6i	0.204661	−	0.118161i
$185$	3.47250e6	+	6.01454e6i	0.0403219	+	0.0698395i
$186$		0			0
$187$			3.99610e6i			0.0446880i
$188$	−9.06147e7	−	5.23164e7i	−0.994595	−	0.574230i
$189$		0			0
$190$		−	4.54080e7i		−	0.480280i
$191$	−7.01190e6	+	1.21450e7i	−0.0728147	+	0.126119i	−0.900134	−	0.435613i	$-0.856532\pi$
$191$	−7.01190e6	+	1.21450e7i	−0.0728147	+	0.126119i	0.827319	+	0.561732i	$0.189865\pi$
$192$		0			0
$193$	5.19935e7	−	3.00185e7i	0.520593	−	0.300565i	−0.216584	−	0.976264i	$-0.569492\pi$
$193$	5.19935e7	−	3.00185e7i	0.520593	−	0.300565i	0.737177	+	0.675699i	$0.236158\pi$
$194$	8.13913e7			0.800336
$195$		0			0
$196$	1.78855e8			1.69670
$197$	3.93786e7	−	2.27353e7i	0.366968	−	0.211869i	−0.305165	−	0.952300i	$-0.598712\pi$
$197$	3.93786e7	−	2.27353e7i	0.366968	−	0.211869i	0.672133	+	0.740430i	$0.265378\pi$
$198$		0			0
$199$	6.36201e7	−	1.10193e8i	0.572280	−	0.991218i	−0.424052	−	0.905638i	$-0.639392\pi$
$199$	6.36201e7	−	1.10193e8i	0.572280	−	0.991218i	0.996331	−	0.0855795i	$-0.0272742\pi$
$200$		−	2.73071e7i		−	0.241363i
$201$		0			0
$202$	−2.02361e7	−	1.16833e7i	−0.172742	−	0.0997325i
$203$		−	3.23213e8i		−	2.71177i
$204$		0			0
$205$	3.24117e7	+	5.61386e7i	0.262762	+	0.455117i
$206$	−9.47141e7	+	5.46832e7i	−0.754883	+	0.435832i
$207$		0			0
$208$	9.78371e7	+	2.67974e7i	0.753845	+	0.206477i
$209$	−4.11736e7			−0.311966
$210$		0			0
$211$	−3.31029e7	−	5.73360e7i	−0.242593	−	0.420183i	0.718859	−	0.695156i	$-0.244665\pi$
$211$	−3.31029e7	−	5.73360e7i	−0.242593	−	0.420183i	−0.961452	+	0.274973i	$0.911331\pi$
$212$	1.28259e8	−	2.22151e8i	0.924510	−	1.60130i
$213$		0			0
$214$	9.56665e7	+	5.52331e7i	0.667285	+	0.385257i
$215$	−6.44760e7	−	3.72252e7i	−0.442449	−	0.255448i
$216$		0			0
$217$	1.09600e8	−	1.89833e8i	0.728118	−	1.26114i
$218$	1.03947e8	+	1.80042e8i	0.679541	+	1.17700i
$219$		0			0
$220$	2.05325e7			0.130006
$221$	−5.59891e6	−	2.13684e7i	−0.0348924	−	0.133168i
$222$		0			0
$223$	−1.66009e8	+	9.58456e7i	−1.00246	+	0.578769i	−0.908974	−	0.416852i	$-0.863133\pi$
$223$	−1.66009e8	+	9.58456e7i	−1.00246	+	0.578769i	−0.0934824	+	0.995621i	$0.529800\pi$
$224$	1.87288e8	+	3.24393e8i	1.11338	+	1.92843i
$225$		0			0
$226$			1.98870e8i			1.14601i
$227$	−4.86806e7	−	2.81058e7i	−0.276226	−	0.159479i	0.355487	−	0.934681i	$-0.384315\pi$
$227$	−4.86806e7	−	2.81058e7i	−0.276226	−	0.159479i	−0.631714	+	0.775202i	$0.717648\pi$
$228$		0			0
$229$		−	2.40345e8i		−	1.32255i	−0.750145	−	0.661274i	$-0.770016\pi$
$229$		−	2.40345e8i		−	1.32255i	0.750145	−	0.661274i	$-0.229984\pi$
$230$	3.99833e7	−	6.92531e7i	0.216686	−	0.375311i
$231$		0			0
$232$	−7.80483e7	+	4.50612e7i	−0.410351	+	0.236916i
$233$	8.29632e7			0.429675			0.214837	−	0.976650i	$-0.431078\pi$
$233$	8.29632e7			0.429675			0.214837	+	0.976650i	$0.431078\pi$
$234$		0			0
$235$	−6.52309e7			−0.327881
$236$	6.48153e7	−	3.74211e7i	0.320986	−	0.185321i
$237$		0			0
$238$	3.29992e7	−	5.71563e7i	0.158666	−	0.274818i
$239$		−	1.71336e8i		−	0.811812i	−0.913915	−	0.405906i	$-0.866956\pi$
$239$		−	1.71336e8i		−	0.811812i	0.913915	−	0.405906i	$-0.133044\pi$
$240$		0			0
$241$	−3.88143e7	−	2.24094e7i	−0.178621	−	0.103127i	0.408024	−	0.912971i	$-0.366218\pi$
$241$	−3.88143e7	−	2.24094e7i	−0.178621	−	0.103127i	−0.586644	+	0.809845i	$0.699551\pi$
$242$			2.91514e8i			1.32222i
$243$		0			0
$244$	1.67348e8	+	2.89855e8i	0.737489	+	1.27737i
$245$	9.65642e7	−	5.57514e7i	0.419503	−	0.242200i
$246$		0			0
$247$	2.20169e8	−	5.76881e7i	0.929643	−	0.243583i
$248$	−6.11202e7			−0.254451
$249$		0			0
$250$	−1.16408e8	−	2.01625e8i	−0.471188	−	0.816121i
$251$	1.23172e8	−	2.13340e8i	0.491647	−	0.851558i	−0.508307	−	0.861176i	$-0.669728\pi$
$251$	1.23172e8	−	2.13340e8i	0.491647	−	0.851558i	0.999954	+	0.00961855i	$0.00306173\pi$
$252$		0			0
$253$	−6.27951e7	−	3.62548e7i	−0.243783	−	0.140748i
$254$	−4.57604e8	−	2.64198e8i	−1.75215	−	1.01161i
$255$		0			0
$256$	−7.20273e7	+	1.24755e8i	−0.268323	+	0.464749i
$257$	−5.62993e7	−	9.75132e7i	−0.206889	−	0.358342i	0.743844	−	0.668353i	$-0.233000\pi$
$257$	−5.62993e7	−	9.75132e7i	−0.206889	−	0.358342i	−0.950733	+	0.310011i	$0.899667\pi$
$258$		0			0
$259$	−1.04005e8			−0.371969
$260$	−1.09794e8	+	2.87679e7i	−0.387411	+	0.101508i
$261$		0			0
$262$	2.10219e8	−	1.21370e8i	0.722132	−	0.416923i
$263$	−1.74722e8	−	3.02628e8i	−0.592247	−	1.02580i	−0.993929	−	0.110022i	$-0.964908\pi$
$263$	−1.74722e8	−	3.02628e8i	−0.592247	−	1.02580i	0.401682	−	0.915779i	$-0.368426\pi$
$264$		0			0
$265$		−	1.59920e8i		−	0.527888i
$266$	5.88907e8	+	3.40006e8i	1.91850	+	1.10764i
$267$		0			0
$268$			3.42232e8i			1.08605i
$269$	−1.70019e8	+	2.94481e8i	−0.532554	+	0.922411i	0.466724	+	0.884403i	$0.345434\pi$
$269$	−1.70019e8	+	2.94481e8i	−0.532554	+	0.922411i	−0.999277	+	0.0380072i	$0.987899\pi$
$270$		0			0
$271$	−3.82994e8	+	2.21121e8i	−1.16896	+	0.674898i	−0.953434	−	0.301600i	$-0.902479\pi$
$271$	−3.82994e8	+	2.21121e8i	−1.16896	+	0.674898i	−0.215524	+	0.976499i	$0.569146\pi$
$272$	3.57108e7			0.107599
$273$		0			0
$274$	−8.84895e8			−2.59875
$275$	−8.58689e7	+	4.95764e7i	−0.248984	+	0.143751i
$276$		0			0
$277$	−5.03144e7	+	8.71472e7i	−0.142237	+	0.246362i	−0.928339	−	0.371735i	$-0.878763\pi$
$277$	−5.03144e7	+	8.71472e7i	−0.142237	+	0.246362i	0.786102	+	0.618097i	$0.212096\pi$
$278$			9.18765e8i			2.56476i
$279$		0			0
$280$	−4.57207e7	−	2.63968e7i	−0.124468	−	0.0718619i
$281$		−	2.13226e8i		−	0.573281i	−0.958038	−	0.286640i	$-0.907462\pi$
$281$		−	2.13226e8i		−	0.573281i	0.958038	−	0.286640i	$-0.0925385\pi$
$282$		0			0
$283$	−8.69416e7	−	1.50587e8i	−0.228021	−	0.394944i	0.729200	−	0.684300i	$-0.239892\pi$
$283$	−8.69416e7	−	1.50587e8i	−0.228021	−	0.394944i	−0.957222	+	0.289356i	$0.906559\pi$
$284$	−5.29841e7	+	3.05904e7i	−0.137256	+	0.0792448i
$285$		0			0
$286$	4.81095e7	+	1.83612e8i	0.121605	+	0.464108i
$287$	−9.70767e8			−2.42398
$288$		0			0
$289$	2.01281e8	+	3.48629e8i	0.490524	+	0.849613i
$290$	−1.80445e8	+	3.12540e8i	−0.434462	+	0.752510i
$291$		0			0
$292$	−6.69022e7	−	3.86260e7i	−0.157254	−	0.0907904i
$293$	1.13850e8	+	6.57312e7i	0.264421	+	0.152663i	0.626349	−	0.779542i	$-0.284548\pi$
$293$	1.13850e8	+	6.57312e7i	0.264421	+	0.152663i	−0.361929	+	0.932206i	$0.617882\pi$
$294$		0			0
$295$	2.33293e7	−	4.04076e7i	0.0529085	−	0.0916402i
$296$	1.45001e7	+	2.51148e7i	0.0324974	+	0.0562872i
$297$		0			0
$298$	−7.58996e8			−1.66143
$299$	3.86582e8	+	1.05884e8i	0.836359	+	0.229077i
$300$		0			0
$301$	9.65566e8	−	5.57470e8i	2.04079	−	1.17825i
$302$	−3.05836e8	−	5.29723e8i	−0.638946	−	1.10669i
$303$		0			0
$304$			3.67944e8i			0.751147i
$305$	1.80703e8	+	1.04329e8i	0.364684	+	0.210550i
$306$		0			0
$307$		−	7.71793e8i		−	1.52236i	−0.648542	−	0.761179i	$-0.724621\pi$
$307$		−	7.71793e8i		−	1.52236i	0.648542	−	0.761179i	$-0.275379\pi$
$308$	−1.53743e8	+	2.66291e8i	−0.299825	+	0.519312i
$309$		0			0
$310$	−2.11962e8	+	1.22376e8i	−0.404103	+	0.233309i
$311$	−3.88587e8			−0.732533			−0.366267	−	0.930510i	$-0.619364\pi$
$311$	−3.88587e8			−0.732533			−0.366267	+	0.930510i	$0.619364\pi$
$312$		0			0
$313$	−5.42552e8			−1.00008			−0.500042	−	0.866001i	$-0.666682\pi$
$313$	−5.42552e8			−1.00008			−0.500042	+	0.866001i	$0.666682\pi$
$314$	−9.09796e8	+	5.25271e8i	−1.65840	+	0.957479i
$315$		0			0
$316$	−1.45383e8	+	2.51811e8i	−0.259185	+	0.448922i
$317$			9.56858e7i			0.168710i	0.996436	+	0.0843549i	$0.0268829\pi$
$317$			9.56858e7i			0.168710i	−0.996436	+	0.0843549i	$0.973117\pi$
$318$		0			0
$319$	2.83395e8	+	1.63618e8i	0.488793	+	0.282205i
$320$		−	2.63321e8i		−	0.449221i
$321$		0			0
$322$	5.98773e8	+	1.03711e9i	0.999463	+	1.73112i
$323$	6.93892e7	−	4.00619e7i	0.114573	−	0.0661489i
$324$		0			0
$325$	3.89707e8	−	3.85411e8i	0.629719	−	0.622777i
$326$	4.72295e8			0.755008
$327$		0			0
$328$	1.35341e8	+	2.34417e8i	0.211773	+	0.366802i
$329$	4.88435e8	−	8.45995e8i	0.756173	−	1.30973i
$330$		0			0
$331$	1.93482e8	+	1.11707e8i	0.293253	+	0.169310i	0.639408	−	0.768868i	$-0.279179\pi$
$331$	1.93482e8	+	1.11707e8i	0.293253	+	0.169310i	−0.346155	+	0.938177i	$0.612513\pi$
$332$	6.00963e8	+	3.46966e8i	0.901290	+	0.520360i
$333$		0			0
$334$	7.16425e8	−	1.24088e9i	1.05210	−	1.82229i
$335$	1.06678e8	+	1.84772e8i	0.155031	+	0.268522i
$336$		0			0
$337$	5.78709e8			0.823674			0.411837	−	0.911257i	$-0.364887\pi$
$337$	5.78709e8			0.823674			0.411837	+	0.911257i	$0.364887\pi$
$338$	−5.14514e8	−	9.14425e8i	−0.724751	−	1.28807i
$339$		0			0
$340$	−3.46031e7	+	1.99781e7i	−0.0477462	+	0.0275663i
$341$	1.10964e8	+	1.92196e8i	0.151546	+	0.262485i
$342$		0			0
$343$			5.04190e8i			0.674629i
$344$	−2.69232e8	−	1.55441e8i	−0.356592	−	0.205878i
$345$		0			0
$346$		−	1.79259e8i		−	0.232656i
$347$	2.73783e8	−	4.74206e8i	0.351765	−	0.609275i	−0.634794	−	0.772682i	$-0.718915\pi$
$347$	2.73783e8	−	4.74206e8i	0.351765	−	0.609275i	0.986559	+	0.163407i	$0.0522482\pi$
$348$		0			0
$349$	−9.74125e8	+	5.62411e8i	−1.22666	+	0.708215i	−0.966331	−	0.257304i	$-0.917166\pi$
$349$	−9.74125e8	+	5.62411e8i	−1.22666	+	0.708215i	−0.260333	+	0.965519i	$0.583833\pi$
$350$	1.63758e9			2.04157
$351$		0			0
$352$	−3.79240e8			−0.463463
$353$	8.05864e8	−	4.65266e8i	0.975102	−	0.562976i	0.0743143	−	0.997235i	$-0.476323\pi$
$353$	8.05864e8	−	4.65266e8i	0.975102	−	0.562976i	0.900788	+	0.434259i	$0.142990\pi$
$354$		0			0
$355$	−1.90709e7	+	3.30317e7i	−0.0226241	+	0.0391861i
$356$			5.34622e8i			0.628018i
$357$		0			0
$358$	1.66169e9	+	9.59380e8i	1.91408	+	1.10510i
$359$			8.37591e8i			0.955436i	0.878513	+	0.477718i	$0.158536\pi$
$359$			8.37591e8i			0.955436i	−0.878513	+	0.477718i	$0.841464\pi$
$360$		0			0
$361$	−3.41599e7	−	5.91667e7i	−0.0382157	−	0.0661915i
$362$	−1.08704e9	+	6.27600e8i	−1.20438	+	0.695349i
$363$		0			0
$364$	4.49016e8	−	1.63935e9i	0.487985	−	1.78163i
$365$	−4.81610e7			−0.0518406
$366$		0			0
$367$	−2.90619e8	−	5.03368e8i	−0.306898	−	0.531562i	0.670784	−	0.741652i	$-0.265958\pi$
$367$	−2.90619e8	−	5.03368e8i	−0.306898	−	0.531562i	−0.977682	+	0.210090i	$0.932624\pi$
$368$	−3.23988e8	+	5.61163e8i	−0.338892	+	0.586978i
$369$		0			0
$370$	1.00571e8	+	5.80647e7i	0.103221	+	0.0595945i
$371$	2.07404e9	+	1.19745e9i	2.10867	+	1.21744i
$372$		0			0
$373$	−1.23831e8	+	2.14481e8i	−0.123551	+	0.213997i	−0.921166	−	0.389170i	$-0.872762\pi$
$373$	−1.23831e8	+	2.14481e8i	−0.123551	+	0.213997i	0.797614	+	0.603168i	$0.206095\pi$
$374$	3.34100e7	+	5.78678e7i	0.0330237	+	0.0571987i
$375$		0			0
$376$	−2.72384e8			−0.264255
$377$	−1.74465e9	−	4.77857e8i	−1.67692	−	0.459307i
$378$		0			0
$379$	−1.23128e9	+	7.10878e8i	−1.16177	+	0.670746i	−0.951726	−	0.306947i	$-0.900692\pi$
$379$	−1.23128e9	+	7.10878e8i	−1.16177	+	0.670746i	−0.210039	+	0.977693i	$0.567359\pi$
$380$	−2.05843e8	−	3.56531e8i	−0.192440	−	0.333315i
$381$		0			0
$382$			2.34496e8i			0.215236i
$383$	−9.66671e8	−	5.58108e8i	−0.879190	−	0.507601i	−0.00879891	−	0.999961i	$-0.502801\pi$
$383$	−9.66671e8	−	5.58108e8i	−0.879190	−	0.507601i	−0.870391	+	0.492361i	$0.836134\pi$
$384$		0			0
$385$			1.91695e8i			0.171198i
$386$	5.01948e8	−	8.69399e8i	0.444225	−	0.769421i
$387$		0			0
$388$	6.39063e8	−	3.68963e8i	0.555434	−	0.320680i
$389$	−2.16836e9			−1.86770			−0.933851	−	0.357661i	$-0.883574\pi$
$389$	−2.16836e9			−1.86770			−0.933851	+	0.357661i	$0.883574\pi$
$390$		0			0
$391$	1.41103e8			0.119377
$392$	4.03222e8	−	2.32800e8i	0.338098	−	0.195201i
$393$		0			0
$394$	3.80163e8	−	6.58462e8i	0.313136	−	0.542368i
$395$			1.81272e8i			0.147993i
$396$		0			0
$397$	2.54448e8	+	1.46906e8i	0.204095	+	0.117834i	0.598564	−	0.801075i	$-0.295738\pi$
$397$	2.54448e8	+	1.46906e8i	0.204095	+	0.117834i	−0.394469	+	0.918909i	$0.629072\pi$
$398$		−	2.12762e9i		−	1.69162i
$399$		0			0
$400$	4.43035e8	+	7.67359e8i	0.346121	+	0.599500i
$401$	4.32014e8	−	2.49424e8i	0.334574	−	0.193167i	−0.323296	−	0.946298i	$-0.604791\pi$
$401$	4.32014e8	−	2.49424e8i	0.334574	−	0.193167i	0.657870	+	0.753131i	$0.271458\pi$
$402$		0			0
$403$	−8.62647e8	−	8.72263e8i	−0.656547	−	0.663865i
$404$	−2.11851e8			−0.159844
$405$		0			0
$406$	−2.70227e9	−	4.68047e9i	−2.00395	−	3.47095i
$407$	5.26501e7	−	9.11926e7i	0.0387096	−	0.0670469i
$408$		0			0
$409$	−7.68986e7	−	4.43974e7i	−0.0555760	−	0.0320868i	0.471955	−	0.881623i	$-0.343549\pi$
$409$	−7.68986e7	−	4.43974e7i	−0.0555760	−	0.0320868i	−0.527531	+	0.849536i	$0.676882\pi$
$410$	9.38711e8	+	5.41965e8i	0.672649	+	0.388354i
$411$		0			0
$412$	−4.95780e8	+	8.58716e8i	−0.349260	+	0.604936i
$413$	3.49370e8	+	6.05127e8i	0.244040	+	0.422690i
$414$		0			0
$415$	4.32616e8			0.297121
$416$	2.02792e9	−	5.31350e8i	1.38110	−	0.361872i
$417$		0			0
$418$	−5.96238e8	+	3.44238e8i	−0.399303	+	0.230538i
$419$	7.78083e7	+	1.34768e8i	0.0516746	+	0.0895030i	0.890706	−	0.454580i	$-0.150211\pi$
$419$	7.78083e7	+	1.34768e8i	0.0516746	+	0.0895030i	−0.839031	+	0.544083i	$0.816877\pi$
$420$		0			0
$421$			2.18824e9i			1.42925i	0.699509	+	0.714624i	$0.253402\pi$
$421$			2.18824e9i			1.42925i	−0.699509	+	0.714624i	$0.746598\pi$
$422$	−9.58732e8	−	5.53524e8i	−0.621017	−	0.358545i
$423$		0			0
$424$		−	6.67775e8i		−	0.425451i
$425$	9.64756e7	−	1.67101e8i	0.0609616	−	0.105589i
$426$		0			0
$427$	−2.70614e9	+	1.56239e9i	−1.68210	+	0.971162i
$428$	1.00153e9			0.617462
$429$		0			0
$430$	−1.24491e9			−0.755089
$431$	8.28504e7	−	4.78337e7i	0.0498453	−	0.0287782i	−0.474870	−	0.880056i	$-0.657505\pi$
$431$	8.28504e7	−	4.78337e7i	0.0498453	−	0.0287782i	0.524716	+	0.851278i	$0.324172\pi$
$432$		0			0
$433$	4.81515e8	−	8.34009e8i	0.285038	−	0.493700i	−0.687580	−	0.726108i	$-0.741327\pi$
$433$	4.81515e8	−	8.34009e8i	0.285038	−	0.493700i	0.972618	+	0.232408i	$0.0746605\pi$
$434$		−	3.66531e9i		−	2.15227i
$435$		0			0
$436$	1.63233e9	+	9.42428e8i	0.943205	+	0.544560i
$437$			1.45385e9i			0.833365i
$438$		0			0
$439$	1.02158e9	+	1.76942e9i	0.576296	+	0.998174i	0.995900	+	0.0904662i	$0.0288357\pi$
$439$	1.02158e9	+	1.76942e9i	0.576296	+	0.998174i	−0.419604	+	0.907707i	$0.637831\pi$
$440$	4.62898e7	−	2.67254e7i	0.0259061	−	0.0149569i
$441$		0			0
$442$	−2.59732e8	−	2.62627e8i	−0.143070	−	0.144665i
$443$	−9.64971e8			−0.527353			−0.263676	−	0.964611i	$-0.584935\pi$
$443$	−9.64971e8			−0.527353			−0.263676	+	0.964611i	$0.584935\pi$
$444$		0			0
$445$	1.66649e8	+	2.88644e8i	0.0896483	+	0.155275i
$446$	−1.60266e9	+	2.77589e9i	−0.855402	+	1.48160i
$447$		0			0
$448$	3.41507e9	+	1.97169e9i	1.79443	+	1.03601i
$449$	1.74162e9	+	1.00552e9i	0.908010	+	0.524240i	0.879790	−	0.475362i	$-0.157683\pi$
$449$	1.74162e9	+	1.00552e9i	0.908010	+	0.524240i	0.0282196	+	0.999602i	$0.491016\pi$
$450$		0			0
$451$	4.91426e8	−	8.51175e8i	0.252255	−	0.436919i
$452$	9.01515e8	+	1.56147e9i	0.459186	+	0.795333i
$453$		0			0
$454$	−9.39930e8			−0.471411
$455$	−2.68582e8	−	1.02506e9i	−0.133671	−	0.510161i
$456$		0			0
$457$	2.67986e9	−	1.54722e9i	1.31343	−	0.758307i	0.330764	−	0.943713i	$-0.392693\pi$
$457$	2.67986e9	−	1.54722e9i	1.31343	−	0.758307i	0.982662	+	0.185406i	$0.0593601\pi$
$458$	−2.00944e9	−	3.48046e9i	−0.977341	−	1.69280i
$459$		0			0
$460$		−	7.25009e8i		−	0.347289i
$461$	2.17221e9	+	1.25413e9i	1.03264	+	0.596194i	0.917740	−	0.397183i	$-0.130012\pi$
$461$	2.17221e9	+	1.25413e9i	1.03264	+	0.596194i	0.114899	+	0.993377i	$0.463345\pi$
$462$		0			0
$463$		−	8.14250e8i		−	0.381263i	−0.981662	−	0.190631i	$-0.938947\pi$
$463$		−	8.14250e8i		−	0.381263i	0.981662	−	0.190631i	$-0.0610535\pi$
$464$	1.46216e9	−	2.53254e9i	0.679488	−	1.17691i
$465$		0			0
$466$	1.20140e9	−	6.93626e8i	0.549965	−	0.317523i
$467$	2.48449e9			1.12883			0.564413	−	0.825492i	$-0.309102\pi$
$467$	2.48449e9			1.12883			0.564413	+	0.825492i	$0.309102\pi$
$468$		0			0
$469$	−3.19514e9			−1.43016
$470$	−9.44613e8	+	5.45373e8i	−0.419673	+	0.242299i
$471$		0			0
$472$	9.74160e7	−	1.68729e8i	0.0426416	−	0.0738574i
$473$			1.12882e9i			0.490468i
$474$		0			0
$475$	1.72171e9	+	9.94032e8i	0.737112	+	0.425572i
$476$		−	5.98367e8i		−	0.254298i
$477$		0			0
$478$	−1.43248e9	−	2.48113e9i	−0.599916	−	1.03909i
$479$	−3.84575e9	+	2.22034e9i	−1.59884	+	0.923094i	−0.607135	+	0.794599i	$0.707681\pi$
$479$	−3.84575e9	+	2.22034e9i	−1.59884	+	0.923094i	−0.991710	+	0.128495i	$0.958985\pi$
$480$		0			0
$481$	−1.53768e8	+	5.61404e8i	−0.0630024	+	0.230021i
$482$	−7.49430e8			−0.304836
$483$		0			0
$484$	1.32149e9	+	2.28889e9i	0.529791	+	0.917626i
$485$	2.30021e8	−	3.98409e8i	0.0915529	−	0.158574i
$486$		0			0
$487$	3.19931e9	+	1.84712e9i	1.25518	+	0.724677i	0.972133	−	0.234430i	$-0.0753224\pi$
$487$	3.19931e9	+	1.84712e9i	1.25518	+	0.724677i	0.283044	+	0.959107i	$0.408656\pi$
$488$	7.54560e8	+	4.35645e8i	0.293917	+	0.169693i
$489$		0			0
$490$	9.32235e8	−	1.61468e9i	0.357964	−	0.620012i
$491$	1.54685e9	+	2.67922e9i	0.589743	+	1.02147i	0.994266	+	0.106937i	$0.0341044\pi$
$491$	1.54685e9	+	2.67922e9i	0.589743	+	1.02147i	−0.404523	+	0.914528i	$0.632562\pi$
$492$		0			0
$493$	−6.36802e8			−0.239354
$494$	2.70597e9	−	2.67614e9i	1.00990	−	0.998767i
$495$		0			0
$496$	1.71754e9	−	9.91624e8i	0.632007	−	0.364889i
$497$	−2.85597e8	−	4.94669e8i	−0.104353	−	0.180745i
$498$		0			0
$499$			2.44557e9i			0.881107i	0.897726	+	0.440554i	$0.145218\pi$
$499$			2.44557e9i			0.881107i	−0.897726	+	0.440554i	$0.854782\pi$
$500$	−1.82801e9	−	1.05540e9i	−0.654010	−	0.377593i
$501$		0			0
$502$		−	4.11919e9i		−	1.45328i
$503$	1.72252e9	−	2.98349e9i	0.603498	−	1.04529i	−0.388789	−	0.921327i	$-0.627107\pi$
$503$	1.72252e9	−	2.98349e9i	0.603498	−	1.04529i	0.992287	−	0.123962i	$-0.0395602\pi$
$504$		0			0
$505$	−1.14379e8	+	6.60369e7i	−0.0395209	+	0.0228174i
$506$	−1.21245e9			−0.416043
$507$		0			0
$508$	−4.79064e9			−1.62133
$509$	−1.62877e9	+	9.40371e8i	−0.547454	+	0.316073i	−0.748095	−	0.663592i	$-0.769031\pi$
$509$	−1.62877e9	+	9.40371e8i	−0.547454	+	0.316073i	0.200640	+	0.979665i	$0.435698\pi$
$510$		0			0
$511$	3.60619e8	−	6.24611e8i	0.119557	−	0.207079i
$512$			4.03595e9i			1.32893i
$513$		0			0
$514$	−1.63055e9	−	9.41397e8i	−0.529618	−	0.305775i
$515$			6.18165e8i			0.199425i
$516$		0			0
$517$	4.94516e8	+	8.56527e8i	0.157385	+	0.272599i
$518$	−1.50611e9	+	8.69552e8i	−0.476104	+	0.274879i
$519$		0			0
$520$	−2.10082e8	+	2.07766e8i	−0.0655204	+	0.0647981i
$521$	−7.91865e8			−0.245312			−0.122656	−	0.992449i	$-0.539141\pi$
$521$	−7.91865e8			−0.245312			−0.122656	+	0.992449i	$0.539141\pi$
$522$		0			0
$523$	−1.03050e8	−	1.78488e8i	−0.0314986	−	0.0545572i	0.849846	−	0.527030i	$-0.176695\pi$
$523$	−1.03050e8	−	1.78488e8i	−0.0314986	−	0.0545572i	−0.881345	+	0.472473i	$0.843361\pi$
$524$	1.10039e9	−	1.90592e9i	0.334107	−	0.578690i
$525$		0			0
$526$	−5.06033e9	−	2.92158e9i	−1.51610	−	0.875322i
$527$	−3.74013e8	−	2.15937e8i	−0.111314	−	0.0642672i
$528$		0			0
$529$	4.22245e8	−	7.31351e8i	0.124014	−	0.214798i
$530$	−1.33703e9	−	2.31581e9i	−0.390101	−	0.675675i
$531$		0			0
$532$	6.16525e9			1.77525
$533$	−1.43524e9	+	5.24004e9i	−0.410562	+	1.49896i
$534$		0			0
$535$	5.40729e8	−	3.12190e8i	0.152666	−	0.0881416i
$536$	4.45455e8	+	7.71551e8i	0.124947	+	0.216415i
$537$		0			0
$538$			5.68587e9i			1.57420i
$539$	−1.46411e9	−	8.45303e8i	−0.402729	−	0.232515i
$540$		0			0
$541$			5.13810e9i			1.39512i	0.716525	+	0.697561i	$0.245731\pi$
$541$			5.13810e9i			1.39512i	−0.716525	+	0.697561i	$0.754269\pi$
$542$	−3.69744e9	+	6.40415e9i	−0.997478	+	1.72768i
$543$		0			0
$544$	6.39127e8	−	3.69000e8i	0.170212	−	0.0982722i
$545$	1.17507e9			0.310939
$546$		0			0
$547$	3.45399e8			0.0902331			0.0451165	−	0.998982i	$-0.485634\pi$
$547$	3.45399e8			0.0902331			0.0451165	+	0.998982i	$0.485634\pi$
$548$	−6.94795e9	+	4.01140e9i	−1.80354	+	1.04127i
$549$		0			0
$550$	−8.28982e8	+	1.43584e9i	−0.212459	+	0.367990i
$551$		−	6.56126e9i		−	1.67092i
$552$		0			0
$553$	−2.35095e9	−	1.35732e9i	−0.591162	−	0.341307i
$554$			1.68265e9i			0.420444i
$555$		0			0
$556$	4.16494e9	+	7.21389e9i	1.02765	+	1.77995i
$557$	3.11237e9	−	1.79693e9i	0.763128	−	0.440592i	−0.0672895	−	0.997733i	$-0.521435\pi$
$557$	3.11237e9	−	1.79693e9i	0.763128	−	0.440592i	0.830418	+	0.557141i	$0.188102\pi$
$558$		0			0
$559$	−1.58158e9	−	6.03616e9i	−0.382957	−	1.46157i
$560$	1.71307e9			0.412207
$561$		0			0
$562$	−1.78271e9	−	3.08774e9i	−0.423645	−	0.733775i
$563$	−6.38718e8	+	1.10629e9i	−0.150845	+	0.261270i	−0.931538	−	0.363644i	$-0.881533\pi$
$563$	−6.38718e8	+	1.10629e9i	−0.150845	+	0.261270i	0.780694	+	0.624914i	$0.214866\pi$
$564$		0			0
$565$	9.73462e8	+	5.62028e8i	0.227065	+	0.131096i
$566$	−2.51801e9	−	1.45378e9i	−0.583715	−	0.337008i
$567$		0			0
$568$	−7.96339e7	+	1.37930e8i	−0.0182339	+	0.0315820i
$569$	2.39425e9	+	4.14696e9i	0.544849	+	0.943705i	0.998616	+	0.0525855i	$0.0167462\pi$
$569$	2.39425e9	+	4.14696e9i	0.544849	+	0.943705i	−0.453768	+	0.891120i	$0.649920\pi$
$570$		0			0
$571$	−1.93902e9			−0.435869			−0.217935	−	0.975963i	$-0.569932\pi$
$571$	−1.93902e9			−0.435869			−0.217935	+	0.975963i	$0.569932\pi$
$572$	1.21009e9	+	1.22358e9i	0.270354	+	0.273367i
$573$		0			0
$574$	−1.40577e10	+	8.11624e9i	−3.10259	+	1.79128i
$575$	1.75056e9	+	3.03206e9i	0.384007	+	0.665119i
$576$		0			0
$577$		−	6.58473e9i		−	1.42699i	−0.700658	−	0.713497i	$-0.747110\pi$
$577$		−	6.58473e9i		−	1.42699i	0.700658	−	0.713497i	$-0.252890\pi$
$578$	5.82953e9	+	3.36568e9i	1.25570	+	0.724980i
$579$		0			0
$580$			3.27197e9i			0.696324i
$581$	−3.23934e9	+	5.61070e9i	−0.685235	+	1.18686i
$582$		0			0
$583$	−2.09986e9	+	1.21235e9i	−0.438884	+	0.253390i
$584$	−2.01105e8			−0.0417809
$585$		0			0
$586$	2.19822e9			0.451263
$587$	1.06499e9	−	6.14875e8i	0.217327	−	0.125474i	−0.387385	−	0.921918i	$-0.626622\pi$
$587$	1.06499e9	−	6.14875e8i	0.217327	−	0.125474i	0.604712	+	0.796444i	$0.293288\pi$
$588$		0			0
$589$	2.22489e9	−	3.85363e9i	0.448648	−	0.777081i
$590$		−	7.80193e8i		−	0.156394i
$591$		0			0
$592$	−8.14934e8	−	4.70502e8i	−0.161435	−	0.0932043i
$593$		−	8.85789e9i		−	1.74437i	−0.489174	−	0.872186i	$-0.662702\pi$
$593$		−	8.85789e9i		−	1.74437i	0.489174	−	0.872186i	$-0.337298\pi$
$594$		0			0
$595$	−1.86519e8	−	3.23060e8i	−0.0363006	−	0.0628745i
$596$	−5.95943e9	+	3.44068e9i	−1.15304	+	0.665706i
$597$		0			0
$598$	6.48338e9	−	1.69876e9i	1.23979	−	0.324846i
$599$	−3.97030e9			−0.754795			−0.377398	−	0.926051i	$-0.623181\pi$
$599$	−3.97030e9			−0.754795			−0.377398	+	0.926051i	$0.623181\pi$
$600$		0			0
$601$	−2.97559e8	−	5.15388e8i	−0.0559130	−	0.0968441i	0.836714	−	0.547640i	$-0.184474\pi$
$601$	−2.97559e8	−	5.15388e8i	−0.0559130	−	0.0968441i	−0.892627	+	0.450796i	$0.851140\pi$
$602$	9.32162e9	−	1.61455e10i	1.74142	−	3.01623i
$603$		0			0
$604$	−4.80268e9	−	2.77283e9i	−0.886858	−	0.512028i
$605$	1.42695e9	+	8.23852e8i	0.261979	+	0.151253i
$606$		0			0
$607$	9.78279e7	−	1.69443e8i	0.0177542	−	0.0307512i	−0.857012	−	0.515297i	$-0.827682\pi$
$607$	9.78279e7	−	1.69443e8i	0.0177542	−	0.0307512i	0.874766	+	0.484546i	$0.161015\pi$
$608$	3.80198e9	+	6.58522e9i	0.686036	+	1.18825i
$609$		0			0
$610$	3.48904e9			0.622373
$611$	−3.84441e9	−	3.88726e9i	−0.681844	−	0.689445i
$612$		0			0
$613$	−3.21156e9	+	1.85420e9i	−0.563125	+	0.325120i	−0.754399	−	0.656417i	$-0.772071\pi$
$613$	−3.21156e9	+	1.85420e9i	−0.563125	+	0.325120i	0.191274	+	0.981537i	$0.438738\pi$
$614$	−6.45269e9	−	1.11764e10i	−1.12500	−	1.94855i
$615$		0			0
$616$			8.00458e8i			0.137977i
$617$	1.48566e8	+	8.57749e7i	0.0254638	+	0.0147015i	0.512678	−	0.858581i	$-0.328654\pi$
$617$	1.48566e8	+	8.57749e7i	0.0254638	+	0.0147015i	−0.487214	+	0.873283i	$0.661987\pi$
$618$		0			0
$619$			3.49467e9i			0.592228i	0.955153	+	0.296114i	$0.0956908\pi$
$619$			3.49467e9i			0.592228i	−0.955153	+	0.296114i	$0.904309\pi$
$620$	−1.10951e9	+	1.92173e9i	−0.186965	+	0.323833i
$621$		0			0
$622$	−5.62716e9	+	3.24884e9i	−0.937612	+	0.541330i
$623$	−4.99133e9			−0.827004
$624$		0			0
$625$	4.08972e9			0.670060
$626$	−7.85673e9	+	4.53609e9i	−1.28006	+	0.739046i
$627$		0			0
$628$	−4.76231e9	+	8.24857e9i	−0.767289	+	1.32898i
$629$			2.04914e8i			0.0328317i
$630$		0			0
$631$	2.66315e9	+	1.53757e9i	0.421982	+	0.243631i	0.695925	−	0.718115i	$-0.254995\pi$
$631$	2.66315e9	+	1.53757e9i	0.421982	+	0.243631i	−0.273943	+	0.961746i	$0.588328\pi$
$632$			7.56933e8i			0.119275i
$633$		0			0
$634$	7.99996e8	+	1.38563e9i	0.124674	+	0.215941i
$635$	−2.58648e9	+	1.49331e9i	−0.400868	+	0.231441i
$636$		0			0
$637$	9.01340e9	+	2.46876e9i	1.38166	+	0.378434i
$638$	5.47182e9			0.834180
$639$		0			0
$640$	−6.00733e8	−	1.04050e9i	−0.0905840	−	0.156896i
$641$	6.26097e8	−	1.08443e9i	0.0938942	−	0.162629i	−0.815252	−	0.579106i	$-0.803402\pi$
$641$	6.26097e8	−	1.08443e9i	0.0938942	−	0.162629i	0.909147	+	0.416476i	$0.136735\pi$
$642$		0			0
$643$	−9.07510e9	−	5.23951e9i	−1.34621	−	0.777235i	−0.358500	−	0.933530i	$-0.616712\pi$
$643$	−9.07510e9	−	5.23951e9i	−1.34621	−	0.777235i	−0.987711	+	0.156294i	$0.950045\pi$
$644$	9.40281e9	+	5.42871e9i	1.38726	+	0.800933i
$645$		0			0
$646$	6.69887e8	−	1.16028e9i	0.0977660	−	0.169336i
$647$	4.17465e9	+	7.23071e9i	0.605976	+	1.04958i	0.991896	+	0.127049i	$0.0405506\pi$
$647$	4.17465e9	+	7.23071e9i	0.605976	+	1.04958i	−0.385920	+	0.922532i	$0.626116\pi$
$648$		0			0
$649$	−7.07439e8			−0.101586
$650$	2.42109e9	−	8.83938e9i	0.345792	−	1.26248i
$651$		0			0
$652$	3.70833e9	−	2.14101e9i	0.523977	−	0.302518i
$653$	1.23911e9	+	2.14620e9i	0.174146	+	0.301629i	0.939865	−	0.341545i	$-0.110950\pi$
$653$	1.23911e9	+	2.14620e9i	0.174146	+	0.301629i	−0.765720	+	0.643175i	$0.777617\pi$
$654$		0			0
$655$		−	1.37202e9i		−	0.190772i
$656$	−7.60645e9	−	4.39158e9i	−1.05201	−	0.607376i
$657$		0			0
$658$		−	1.63346e10i		−	2.23520i
$659$	−3.03154e9	+	5.25078e9i	−0.412633	+	0.714701i	−0.995177	−	0.0980979i	$-0.968724\pi$
$659$	−3.03154e9	+	5.25078e9i	−0.412633	+	0.714701i	0.582544	+	0.812799i	$0.302057\pi$
$660$		0			0
$661$	4.58581e9	−	2.64762e9i	0.617606	−	0.356575i	−0.158331	−	0.987386i	$-0.550611\pi$
$661$	4.58581e9	−	2.64762e9i	0.617606	−	0.356575i	0.775936	+	0.630811i	$0.217278\pi$
$662$	3.73577e9			0.500469
$663$		0			0
$664$	1.80647e9			0.239465
$665$	3.32864e9	−	1.92179e9i	0.438926	−	0.253414i
$666$		0			0
$667$	5.77741e9	−	1.00068e10i	0.753864	−	1.30573i
$668$		−	1.29908e10i		−	1.68623i
$669$		0			0
$670$	3.08963e9	+	1.78380e9i	0.396867	+	0.229131i
$671$		−	3.16368e9i		−	0.404263i
$672$		0			0
$673$	2.31409e9	+	4.00813e9i	0.292636	+	0.506861i	0.974432	−	0.224682i	$-0.0721342\pi$
$673$	2.31409e9	+	4.00813e9i	0.292636	+	0.506861i	−0.681796	+	0.731542i	$0.738801\pi$
$674$	8.38033e9	−	4.83838e9i	1.05427	−	0.608682i
$675$		0			0
$676$	−8.18510e9	−	4.84742e9i	−1.01908	−	0.603528i
$677$	1.40888e10			1.74507			0.872536	−	0.488550i	$-0.162474\pi$
$677$	1.40888e10			1.74507			0.872536	+	0.488550i	$0.162474\pi$
$678$		0			0
$679$	3.44470e9	+	5.96640e9i	0.422287	+	0.731422i
$680$	−5.20077e7	+	9.00799e7i	−0.00634287	+	0.0109862i
$681$		0			0
$682$	3.21377e9	+	1.85547e9i	0.387944	+	0.223980i
$683$	−1.04457e10	−	6.03082e9i	−1.25448	−	0.724276i	−0.282486	−	0.959271i	$-0.591159\pi$
$683$	−1.04457e10	−	6.03082e9i	−1.25448	−	0.724276i	−0.971996	+	0.234996i	$0.924492\pi$
$684$		0			0
$685$	−2.50081e9	+	4.33154e9i	−0.297279	+	0.514903i
$686$	4.21536e9	+	7.30121e9i	0.498540	+	0.863496i
$687$		0			0
$688$	1.00876e10			1.18094
$689$	9.53000e9	−	9.42494e9i	1.11001	−	1.09777i
$690$		0			0
$691$	1.79208e9	−	1.03466e9i	0.206626	−	0.119296i	−0.393116	−	0.919489i	$-0.628603\pi$
$691$	1.79208e9	−	1.03466e9i	0.206626	−	0.119296i	0.599742	+	0.800193i	$0.295270\pi$
$692$	−8.12614e8	−	1.40749e9i	−0.0932209	−	0.161463i
$693$		0			0
$694$		−	9.15601e9i		−	1.03980i
$695$	4.49733e9	+	2.59654e9i	0.508169	+	0.293391i
$696$		0			0
$697$			1.91263e9i			0.213952i
$698$	−9.40425e9	+	1.62886e10i	−1.04672	+	1.81297i
$699$		0			0
$700$	1.28578e10	−	7.42347e9i	1.41685	−	0.818019i
$701$	1.66276e10			1.82312			0.911561	−	0.411166i	$-0.134878\pi$
$701$	1.66276e10			1.82312			0.911561	+	0.411166i	$0.134878\pi$
$702$		0			0
$703$	−2.11132e9			−0.229198
$704$	−3.45759e9	+	1.99624e9i	−0.373481	+	0.215629i
$705$		0			0
$706$	7.77985e9	−	1.34751e10i	0.832060	−	1.44117i
$707$		−	1.97788e9i		−	0.210490i
$708$		0			0
$709$	−5.62006e8	−	3.24474e8i	−0.0592214	−	0.0341915i	0.470097	−	0.882615i	$-0.344219\pi$
$709$	−5.62006e8	−	3.24474e8i	−0.0592214	−	0.0341915i	−0.529318	+	0.848423i	$0.677552\pi$
$710$			6.37779e8i			0.0668754i
$711$		0			0
$712$	6.95873e8	+	1.20529e9i	0.0722520	+	0.125144i
$713$	6.78650e9	−	3.91819e9i	0.701185	−	0.404829i
$714$		0			0
$715$	1.03474e9	+	2.83413e8i	0.105867	+	0.0289967i
$716$	1.73962e10			1.77117
$717$		0			0
$718$	7.00281e9	+	1.21292e10i	0.706052	+	1.22292i
$719$	−3.15700e9	+	5.46809e9i	−0.316755	+	0.548636i	−0.979809	−	0.199936i	$-0.935927\pi$
$719$	−3.15700e9	+	5.46809e9i	−0.316755	+	0.548636i	0.663054	+	0.748572i	$0.269260\pi$
$720$		0			0
$721$	−8.01712e9	−	4.62869e9i	−0.796609	−	0.459922i
$722$	−9.89345e8	−	5.71198e8i	−0.0978290	−	0.0564816i
$723$		0			0
$724$	−5.69007e9	+	9.85549e9i	−0.557228	+	0.965147i
$725$	−7.90029e9	−	1.36837e10i	−0.769945	−	1.33358i
$726$		0			0
$727$	−6.79560e9			−0.655930			−0.327965	−	0.944690i	$-0.606363\pi$
$727$	−6.79560e9			−0.655930			−0.327965	+	0.944690i	$0.606363\pi$
$728$	−1.12152e9	−	4.28031e9i	−0.107732	−	0.411164i
$729$		0			0
$730$	−6.97422e8	+	4.02657e8i	−0.0663538	+	0.0383094i
$731$	−1.09834e9	−	1.90238e9i	−0.103998	−	0.180130i
$732$		0			0
$733$			2.19137e9i			0.205519i	0.994706	+	0.102760i	$0.0327672\pi$
$733$			2.19137e9i			0.205519i	−0.994706	+	0.102760i	$0.967233\pi$
$734$	−8.41696e9	−	4.85953e9i	−0.785632	−	0.453585i
$735$		0			0
$736$			1.33911e10i			1.23806i
$737$	1.61746e9	−	2.80152e9i	0.148832	−	0.257785i
$738$		0			0
$739$	1.15158e10	−	6.64866e9i	1.04964	−	0.606008i	0.127089	−	0.991891i	$-0.459437\pi$
$739$	1.15158e10	−	6.64866e9i	1.04964	−	0.606008i	0.922548	+	0.385883i	$0.126103\pi$
$740$	1.05287e9			0.0955137
$741$		0			0
$742$	4.00457e10			3.59867
$743$	−6.00811e9	+	3.46878e9i	−0.537374	+	0.310253i	−0.744014	−	0.668164i	$-0.767080\pi$
$743$	−6.00811e9	+	3.46878e9i	−0.537374	+	0.310253i	0.206640	+	0.978417i	$0.433747\pi$
$744$		0			0
$745$	−2.14501e9	+	3.71527e9i	−0.190056	+	0.329187i
$746$			4.14122e9i			0.365210i
$747$		0			0
$748$	5.24653e8	+	3.02908e8i	0.0458370	+	0.0264640i
$749$			9.35046e9i			0.813105i
$750$		0			0
$751$	−1.07805e10	−	1.86724e10i	−0.928753	−	1.60865i	−0.785412	−	0.618973i	$-0.787549\pi$
$751$	−1.07805e10	−	1.86724e10i	−0.928753	−	1.60865i	−0.143340	−	0.989673i	$-0.545784\pi$
$752$	7.65427e9	−	4.41920e9i	0.656359	−	0.378949i
$753$		0			0
$754$	−2.92596e10	+	7.66653e9i	−2.48581	+	0.651327i
$755$	−3.45731e9			−0.292364
$756$		0			0
$757$	1.81786e9	+	3.14862e9i	0.152309	+	0.263806i	0.932076	−	0.362263i	$-0.117996\pi$
$757$	1.81786e9	+	3.14862e9i	0.152309	+	0.263806i	−0.779767	+	0.626070i	$0.784663\pi$
$758$	−1.18868e10	+	2.05886e10i	−0.991341	+	1.71705i
$759$		0			0
$760$	−9.28134e8	−	5.35859e8i	−0.0766943	−	0.0442795i
$761$	−7.31336e9	−	4.22237e9i	−0.601548	−	0.347304i	0.168102	−	0.985770i	$-0.446236\pi$
$761$	−7.31336e9	−	4.22237e9i	−0.601548	−	0.347304i	−0.769650	+	0.638466i	$0.779569\pi$
$762$		0			0
$763$	−8.79867e9	+	1.52397e10i	−0.717103	+	1.24206i
$764$	1.06302e9	+	1.84120e9i	0.0862410	+	0.149374i
$765$		0			0
$766$	−1.86646e10			−1.50044
$767$	3.78291e9	−	9.91188e8i	0.302720	−	0.0793181i
$768$		0			0
$769$	−8.00338e9	+	4.62075e9i	−0.634645	+	0.366413i	−0.782549	−	0.622589i	$-0.786081\pi$
$769$	−8.00338e9	+	4.62075e9i	−0.634645	+	0.366413i	0.147903	+	0.989002i	$0.452748\pi$
$770$	1.60270e9	+	2.77595e9i	0.126512	+	0.219126i
$771$		0			0
$772$		−	9.10172e9i		−	0.711972i
$773$	−1.01460e10	−	5.85780e9i	−0.790072	−	0.456149i	0.0499156	−	0.998753i	$-0.484105\pi$
$773$	−1.01460e10	−	5.85780e9i	−0.790072	−	0.456149i	−0.839988	+	0.542605i	$0.817438\pi$
$774$		0			0
$775$		−	1.07158e10i		−	0.826931i
$776$	9.60497e8	−	1.66363e9i	0.0737870	−	0.127803i
$777$		0			0
$778$	−3.14002e10	+	1.81289e10i	−2.39058	+	1.38020i
$779$	−1.97067e10			−1.49359
$780$		0			0
$781$	5.78305e8			0.0434389
$782$	2.04333e9	−	1.17972e9i	0.152797	−	0.0882174i
$783$		0			0
$784$	−7.55397e9	+	1.30839e10i	−0.559847	+	0.969683i
$785$			5.93790e9i			0.438116i
$786$		0			0
$787$	−1.12399e10	−	6.48938e9i	−0.821962	−	0.474560i	0.0291303	−	0.999576i	$-0.490726\pi$
$787$	−1.12399e10	−	6.48938e9i	−0.821962	−	0.474560i	−0.851093	+	0.525015i	$0.824060\pi$
$788$		−	6.89342e9i		−	0.501872i
$789$		0			0
$790$	1.51555e9	+	2.62501e9i	0.109364	+	0.189424i
$791$	−1.45782e10	+	8.41671e9i	−1.04733	+	0.604678i
$792$		0			0
$793$	4.43261e9	+	1.69172e10i	0.315648	+	1.20468i
$794$	4.91291e9			0.348311
$795$		0			0
$796$	−9.64493e9	−	1.67055e10i	−0.677802	−	1.17399i
$797$	3.11864e9	−	5.40164e9i	0.218203	−	0.377939i	−0.736056	−	0.676921i	$-0.763314\pi$
$797$	3.11864e9	−	5.40164e9i	0.218203	−	0.377939i	0.954259	+	0.298982i	$0.0966471\pi$
$798$		0			0
$799$	−1.66680e9	−	9.62327e8i	−0.115603	−	0.0667435i
$800$	1.58583e10	+	9.15578e9i	1.09507	+	0.632238i
$801$		0			0
$802$	4.17069e9	−	7.22384e9i	0.285494	−	0.494490i
$803$	3.65109e8	+	6.32387e8i	0.0248839	+	0.0431001i
$804$		0			0
$805$	6.76881e9			0.457327
$806$	−1.97847e10	−	5.41901e9i	−1.33094	−	0.364542i
$807$		0			0
$808$	−4.77612e8	+	2.75749e8i	−0.0318519	+	0.0183897i
$809$	6.80989e9	+	1.17951e10i	0.452189	+	0.783215i	0.998522	−	0.0543535i	$-0.0173098\pi$
$809$	6.80989e9	+	1.17951e10i	0.452189	+	0.783215i	−0.546332	+	0.837568i	$0.683976\pi$
$810$		0			0
$811$			3.36478e9i			0.221505i	0.993848	+	0.110752i	$0.0353261\pi$
$811$			3.36478e9i			0.221505i	−0.993848	+	0.110752i	$0.964674\pi$
$812$	−4.24350e10	−	2.44998e10i	−2.78149	−	1.60590i
$813$		0			0
$814$		−	1.76075e9i		−	0.114423i
$815$	1.33476e9	−	2.31187e9i	0.0863677	−	0.149593i
$816$		0			0
$817$	1.96011e10	−	1.13167e10i	1.25749	−	0.726010i
$818$	−1.48477e9			−0.0948465
$819$		0			0
$820$	9.82734e9			0.622426
$821$	−1.79276e10	+	1.03505e10i	−1.13063	+	0.652771i	−0.944094	−	0.329676i	$-0.893060\pi$
$821$	−1.79276e10	+	1.03505e10i	−1.13063	+	0.652771i	−0.186539	+	0.982448i	$0.559727\pi$
$822$		0			0
$823$	−3.94697e9	+	6.83635e9i	−0.246811	+	0.427489i	−0.962639	−	0.270787i	$-0.912716\pi$
$823$	−3.94697e9	+	6.83635e9i	−0.246811	+	0.427489i	0.715828	+	0.698276i	$0.246049\pi$
$824$			2.58126e9i			0.160726i
$825$		0			0
$826$	1.01185e10	+	5.84193e9i	0.624722	+	0.360683i
$827$			2.15815e9i			0.132682i	0.997797	+	0.0663411i	$0.0211325\pi$
$827$			2.15815e9i			0.132682i	−0.997797	+	0.0663411i	$0.978867\pi$
$828$		0			0
$829$	3.47257e9	+	6.01468e9i	0.211695	+	0.366667i	0.952245	−	0.305335i	$-0.0987683\pi$
$829$	3.47257e9	+	6.01468e9i	0.211695	+	0.366667i	−0.740550	+	0.672001i	$0.765435\pi$
$830$	6.26474e9	−	3.61695e9i	0.380303	−	0.219568i
$831$		0			0
$832$	1.56919e10	−	1.55189e10i	0.944592	−	0.934179i
$833$	3.28992e9			0.197209
$834$		0			0
$835$	−4.04940e9	−	7.01376e9i	−0.240707	−	0.416916i
$836$	−3.12100e9	+	5.40573e9i	−0.184745	+	0.319987i
$837$		0			0
$838$	2.25350e9	+	1.30106e9i	0.132283	+	0.0763734i
$839$	8.97596e9	+	5.18227e9i	0.524704	+	0.302938i	0.738857	−	0.673862i	$-0.235366\pi$
$839$	8.97596e9	+	5.18227e9i	0.524704	+	0.302938i	−0.214153	+	0.976800i	$0.568699\pi$
$840$		0			0
$841$	−1.74486e10	+	3.02218e10i	−1.01152	+	1.75200i
$842$	1.82951e10	+	3.16881e10i	1.05619	+	1.82938i
$843$		0			0
$844$	−1.00369e10			−0.574649
$845$	−5.93017e9	−	6.57374e7i	−0.338118	−	0.00374812i
$846$		0			0
$847$	−2.13695e10	+	1.23377e10i	−1.20837	+	0.697655i
$848$	1.08341e10	+	1.87652e10i	0.610108	+	1.05674i
$849$		0			0
$850$		−	3.22640e9i		−	0.180199i
$851$	−3.22004e9	−	1.85909e9i	−0.179105	−	0.103406i
$852$		0			0
$853$		−	1.25745e10i		−	0.693696i	−0.937921	−	0.346848i	$-0.887252\pi$
$853$		−	1.25745e10i		−	0.693696i	0.937921	−	0.346848i	$-0.112748\pi$
$854$	−2.61252e10	+	4.52501e10i	−1.43535	+	2.48609i
$855$		0			0
$856$	2.25791e9	−	1.30361e9i	0.123041	−	0.0710377i
$857$	2.63377e10			1.42937			0.714687	−	0.699445i	$-0.246569\pi$
$857$	2.63377e10			1.42937			0.714687	+	0.699445i	$0.246569\pi$
$858$		0			0
$859$	−6.43919e9			−0.346621			−0.173311	−	0.984867i	$-0.555446\pi$
$859$	−6.43919e9			−0.346621			−0.173311	+	0.984867i	$0.555446\pi$
$860$	−9.77469e9	+	5.64342e9i	−0.524033	+	0.302550i
$861$		0			0
$862$	7.99842e8	−	1.38537e9i	0.0425332	−	0.0736697i
$863$		−	3.08603e10i		−	1.63442i	−0.576343	−	0.817208i	$-0.695521\pi$
$863$		−	3.08603e10i		−	1.63442i	0.576343	−	0.817208i	$-0.304479\pi$
$864$		0			0
$865$	−8.77466e8	−	5.06605e8i	−0.0460971	−	0.0266142i
$866$		−	1.61031e10i		−	0.842554i
$867$		0			0
$868$	−1.66156e10	−	2.87790e10i	−0.862376	−	1.49368i
$869$	2.38022e9	−	1.37422e9i	0.123041	−	0.0710375i
$870$		0			0
$871$	−4.72388e9	+	1.72468e10i	−0.242234	+	0.884394i
$872$	4.90672e9			0.250601
$873$		0			0
$874$	1.21552e10	+	2.10534e10i	0.615844	+	1.06667i
$875$	9.85344e9	−	1.70667e10i	0.497233	−	0.861232i
$876$		0			0
$877$	8.49967e9	+	4.90729e9i	0.425504	+	0.245665i	0.697429	−	0.716654i	$-0.254327\pi$
$877$	8.49967e9	+	4.90729e9i	0.425504	+	0.245665i	−0.271925	+	0.962318i	$0.587660\pi$
$878$	2.95871e10	+	1.70821e10i	1.47527	+	0.851747i
$879$		0			0
$880$	−8.67196e8	+	1.50203e9i	−0.0428971	+	0.0742999i
$881$	8.85422e9	+	1.53360e10i	0.436249	+	0.755606i	0.997397	−	0.0721101i	$-0.0229733\pi$
$881$	8.85422e9	+	1.53360e10i	0.436249	+	0.755606i	−0.561147	+	0.827716i	$0.689640\pi$
$882$		0			0
$883$	3.61270e10			1.76591			0.882956	−	0.469456i	$-0.155550\pi$
$883$	3.61270e10			1.76591			0.882956	+	0.469456i	$0.155550\pi$
$884$	−3.22989e9	−	8.84661e8i	−0.157255	−	0.0430719i
$885$		0			0
$886$	−1.39738e10	+	8.06778e9i	−0.674989	+	0.389705i
$887$	−8.80542e9	−	1.52514e10i	−0.423660	−	0.733800i	0.572634	−	0.819811i	$-0.305921\pi$
$887$	−8.80542e9	−	1.52514e10i	−0.423660	−	0.733800i	−0.996294	+	0.0860106i	$0.972588\pi$
$888$		0			0
$889$		−	4.47263e10i		−	2.13504i
$890$	4.82651e9	+	2.78658e9i	0.229492	+	0.132497i
$891$		0			0
$892$			2.90607e10i			1.37098i
$893$	9.91529e9	−	1.71738e10i	0.465935	−	0.807023i
$894$		0			0
$895$	9.39228e9	−	5.42264e9i	0.437916	−	0.252831i
$896$	1.79927e10			0.835636
$897$		0			0
$898$	3.36273e10			1.54962
$899$	−3.06276e10	+	1.76828e10i	−1.40590	+	0.811695i
$900$		0			0
$901$	2.35924e9	−	4.08632e9i	0.107457	−	0.186121i
$902$		−	1.64346e10i		−	0.745651i
$903$		0			0
$904$	4.06487e9	+	2.34685e9i	0.183003	+	0.105657i
$905$			7.09468e9i			0.318173i
$906$		0			0
$907$	1.54413e10	+	2.67452e10i	0.687162	+	1.19020i	0.972752	+	0.231848i	$0.0744771\pi$
$907$	1.54413e10	+	2.67452e10i	0.687162	+	1.19020i	−0.285590	+	0.958352i	$0.592190\pi$
$908$	−7.38007e9	+	4.26089e9i	−0.327160	+	0.188886i
$909$		0			0
$910$	−1.24595e10	−	1.25984e10i	−0.548094	−	0.554204i
$911$	−5.82328e9			−0.255184			−0.127592	−	0.991827i	$-0.540725\pi$
$911$	−5.82328e9			−0.255184			−0.127592	+	0.991827i	$0.540725\pi$
$912$		0			0
$913$	−3.27966e9	−	5.68055e9i	−0.142620	−	0.247026i
$914$	2.58715e10	−	4.48108e10i	1.12075	−	1.94120i
$915$		0			0
$916$	−3.15552e10	−	1.82184e10i	−1.35655	−	0.783206i
$917$	1.77940e10	+	1.02734e10i	0.762047	+	0.439968i
$918$		0			0
$919$	1.21661e10	−	2.10724e10i	0.517068	−	0.895589i	−0.482735	−	0.875766i	$-0.660357\pi$
$919$	1.21661e10	−	2.10724e10i	0.517068	−	0.895589i	0.999804	−	0.0198224i	$-0.00631009\pi$
$920$	−9.43683e8	−	1.63451e9i	−0.0399548	−	0.0692037i
$921$		0			0
$922$	4.19412e10			1.76231
$923$	−3.09239e9	+	8.10259e8i	−0.129446	+	0.0339171i
$924$		0			0
$925$	−4.40322e9	+	2.54220e9i	−0.182926	+	0.105612i
$926$	−6.80766e9	−	1.17912e10i	−0.281747	−	0.488000i
$927$		0			0
$928$		−	6.04341e10i		−	2.48236i
$929$	−4.03422e9	−	2.32916e9i	−0.165084	−	0.0953111i	0.415182	−	0.909738i	$-0.363718\pi$
$929$	−4.03422e9	−	2.32916e9i	−0.165084	−	0.0953111i	−0.580266	+	0.814427i	$0.697051\pi$
$930$		0			0
$931$			3.38975e10i			1.37671i
$932$	6.28869e9	−	1.08923e10i	0.254451	−	0.440722i
$933$		0			0
$934$	3.59780e10	−	2.07719e10i	1.44485	−	0.834185i
$935$	3.77682e8			0.0151107
$936$		0			0
$937$	4.24433e10			1.68547			0.842734	−	0.538331i	$-0.180945\pi$
$937$	4.24433e10			1.68547			0.842734	+	0.538331i	$0.180945\pi$
$938$	−4.62691e10	+	2.67135e10i	−1.83055	+	1.05687i
$939$		0			0
$940$	−4.94456e9	+	8.56424e9i	−0.194169	+	0.336311i
$941$		−	2.82397e10i		−	1.10483i	−0.833569	−	0.552416i	$-0.813706\pi$
$941$		−	2.82397e10i		−	1.10483i	0.833569	−	0.552416i	$-0.186294\pi$
$942$		0			0
$943$	−3.00552e10	−	1.73524e10i	−1.16716	−	0.673858i
$944$			6.32197e9i			0.244597i
$945$		0			0
$946$	9.43767e9	+	1.63465e10i	0.362448	+	0.627778i
$947$	1.43781e10	−	8.30119e9i	0.550143	−	0.317625i	−0.199036	−	0.979992i	$-0.563781\pi$
$947$	1.43781e10	−	8.30119e9i	0.550143	−	0.317625i	0.749180	+	0.662367i	$0.230448\pi$
$948$		0			0
$949$	−2.83839e9	−	2.87002e9i	−0.107805	−	0.109007i
$950$	3.32430e10			1.25796
$951$		0			0
$952$	−7.78845e8	−	1.34900e9i	−0.0292565	−	0.0506737i
$953$	−2.12895e10	+	3.68745e10i	−0.796783	+	1.38007i	0.124918	+	0.992167i	$0.460133\pi$
$953$	−2.12895e10	+	3.68745e10i	−0.796783	+	1.38007i	−0.921701	+	0.387902i	$0.873200\pi$
$954$		0			0
$955$	1.14785e9	+	6.62714e8i	0.0426457	+	0.0246215i
$956$	−2.24949e10	−	1.29874e10i	−0.832685	−	0.480751i
$957$		0			0
$958$	−3.71270e10	+	6.43059e10i	−1.36430	+	2.36304i
$959$	−3.74512e10	−	6.48673e10i	−1.37120	−	2.37498i
$960$		0			0
$961$	3.52794e9			0.128230
$962$	2.46698e9	+	9.41532e9i	0.0893414	+	0.340975i
$963$		0			0
$964$	−5.88432e9	+	3.39731e9i	−0.211557	+	0.122142i
$965$	−2.83713e9	−	4.91405e9i	−0.101633	−	0.176033i
$966$		0			0
$967$		−	2.16365e10i		−	0.769474i	−0.923026	−	0.384737i	$-0.874292\pi$
$967$		−	2.16365e10i		−	0.769474i	0.923026	−	0.384737i	$-0.125708\pi$
$968$	5.95851e9	+	3.44015e9i	0.211142	+	0.121903i
$969$		0			0
$970$		−	7.69251e9i		−	0.270624i
$971$	2.89323e9	−	5.01123e9i	0.101418	−	0.175662i	−0.810851	−	0.585253i	$-0.800995\pi$
$971$	2.89323e9	−	5.01123e9i	0.101418	−	0.175662i	0.912269	+	0.409591i	$0.134329\pi$
$972$		0			0
$973$	−6.73502e10	+	3.88846e10i	−2.34393	+	1.35327i
$974$	6.17726e10			2.14210
$975$		0			0
$976$	−2.82719e10			−0.973377
$977$	−9.55076e9	+	5.51413e9i	−0.327647	+	0.189167i	−0.654796	−	0.755806i	$-0.727246\pi$
$977$	−9.55076e9	+	5.51413e9i	−0.327647	+	0.189167i	0.327149	+	0.944973i	$0.393912\pi$
$978$		0			0
$979$	2.52673e9	−	4.37643e9i	0.0860637	−	0.149067i
$980$		−	1.69040e10i		−	0.573719i
$981$		0			0
$982$	4.48001e10	+	2.58653e10i	1.50969	+	0.871622i
$983$			1.85197e10i			0.621864i	0.950432	+	0.310932i	$0.100641\pi$
$983$			1.85197e10i			0.621864i	−0.950432	+	0.310932i	$0.899359\pi$
$984$		0			0
$985$	−2.14877e9	−	3.72178e9i	−0.0716412	−	0.124086i
$986$	−9.22157e9	+	5.32408e9i	−0.306363	+	0.176879i
$987$		0			0
$988$	9.11507e9	−	3.32790e10i	0.300684	−	1.09779i
$989$	3.98590e10			1.31020
$990$		0			0
$991$	7.70120e9	+	1.33389e10i	0.251363	+	0.435373i	0.963901	−	0.266260i	$-0.0857880\pi$
$991$	7.70120e9	+	1.33389e10i	0.251363	+	0.435373i	−0.712539	+	0.701633i	$0.752455\pi$
$992$	2.04929e10	−	3.54948e10i	0.666520	−	1.15445i
$993$		0			0
$994$	−8.27151e9	−	4.77556e9i	−0.267136	−	0.154231i
$995$	−1.04147e10	−	6.01290e9i	−0.335169	−	0.193510i
$996$		0			0
$997$	1.81490e10	−	3.14350e10i	0.579990	−	1.00457i	−0.415490	−	0.909598i	$-0.636390\pi$
$997$	1.81490e10	−	3.14350e10i	0.579990	−	1.00457i	0.995480	−	0.0949739i	$-0.0302768\pi$
$998$	2.04466e10	+	3.54145e10i	0.651124	+	1.12778i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.8.q.b.10.6		14
3.2	odd	2		13.8.e.a.10.2	yes	14
12.11	even	2		208.8.w.a.49.5		14
13.4	even	6	inner	117.8.q.b.82.6		14
39.2	even	12		169.8.a.g.1.3		14
39.11	even	12		169.8.a.g.1.12		14
39.17	odd	6		13.8.e.a.4.2	✓	14
39.23	odd	6		169.8.b.d.168.12		14
39.29	odd	6		169.8.b.d.168.3		14
156.95	even	6		208.8.w.a.17.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.2	✓	14	39.17	odd	6
13.8.e.a.10.2	yes	14	3.2	odd	2
117.8.q.b.10.6		14	1.1	even	1	trivial
117.8.q.b.82.6		14	13.4	even	6	inner
169.8.a.g.1.3		14	39.2	even	12
169.8.a.g.1.12		14	39.11	even	12
169.8.b.d.168.3		14	39.29	odd	6
169.8.b.d.168.12		14	39.23	odd	6
208.8.w.a.17.5		14	156.95	even	6
208.8.w.a.49.5		14	12.11	even	2

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	117.8.q.b.10.6

Level	$117$
Weight	$8$
Character	117.10
Analytic conductor	$36.549$
Analytic rank	$0$
Dimension	$14$
Inner twists	$2$