LMFDB - Embedded newform 180.8.e.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,8,Mod(71,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("180.71");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	180.e (of order $2$, degree $1$, 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:	$56.2293045871$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	180.71
Dual form			180.8.e.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.3101 - 0.285532i) q^{2} +(127.837 + 6.45880i) q^{4} -125.000i q^{5} -1017.66i q^{7} +(-1444.01 - 109.551i) q^{8} +O(q^{10})$	\(q+(-11.3101 - 0.285532i) q^{2} +(127.837 + 6.45880i) q^{4} -125.000i q^{5} -1017.66i q^{7} +(-1444.01 - 109.551i) q^{8} +(-35.6915 + 1413.76i) q^{10} -4949.52 q^{11} -5267.74 q^{13} +(-290.573 + 11509.8i) q^{14} +(16300.6 + 1651.35i) q^{16} +21159.8i q^{17} +12122.1i q^{19} +(807.350 - 15979.6i) q^{20} +(55979.5 + 1413.25i) q^{22} -10926.7 q^{23} -15625.0 q^{25} +(59578.6 + 1504.11i) q^{26} +(6572.83 - 130094. i) q^{28} +175111. i q^{29} -70706.1i q^{31} +(-183890. - 23331.2i) q^{32} +(6041.80 - 239319. i) q^{34} -127207. q^{35} +272479. q^{37} +(3461.26 - 137103. i) q^{38} +(-13693.9 + 180501. i) q^{40} +23618.7i q^{41} -175131. i q^{43} +(-632731. - 31967.9i) q^{44} +(123582. + 3119.92i) q^{46} -1.14576e6 q^{47} -212080. q^{49} +(176720. + 4461.44i) q^{50} +(-673411. - 34023.2i) q^{52} -921020. i q^{53} +618689. i q^{55} +(-111485. + 1.46950e6i) q^{56} +(49999.8 - 1.98052e6i) q^{58} -312509. q^{59} +581361. q^{61} +(-20188.9 + 799693. i) q^{62} +(2.07315e6 + 316385. i) q^{64} +658467. i q^{65} -3.05251e6i q^{67} +(-136667. + 2.70500e6i) q^{68} +(1.43872e6 + 36321.7i) q^{70} +4.72551e6 q^{71} +5.46716e6 q^{73} +(-3.08176e6 - 77801.5i) q^{74} +(-78294.5 + 1.54966e6i) q^{76} +5.03690e6i q^{77} +2.07098e6i q^{79} +(206418. - 2.03757e6i) q^{80} +(6743.89 - 267130. i) q^{82} +854102. q^{83} +2.64497e6 q^{85} +(-50005.4 + 1.98075e6i) q^{86} +(7.14713e6 + 542226. i) q^{88} +7.69685e6i q^{89} +5.36074e6i q^{91} +(-1.39683e6 - 70573.2i) q^{92} +(1.29587e7 + 327152. i) q^{94} +1.51527e6 q^{95} +1.44110e7 q^{97} +(2.39865e6 + 60555.7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 52 q^{4}+O(q^{10}) $ 56 * q + 52 * q^4	$ 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) $ 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−11.3101	−	0.285532i	−0.999681	−	0.0252377i
$2$	−11.3101	−	0.285532i	−0.999681	−	0.0252377i
$3$		0			0
$3$		0			0
$4$	127.837	+	6.45880i	0.998726	+	0.0504594i
$5$		−	125.000i		−	0.447214i
$5$		−	125.000i		−	0.447214i
$6$		0			0
$7$		−	1017.66i		−	1.12139i	−0.828021	−	0.560696i	$-0.810533\pi$
$7$		−	1017.66i		−	1.12139i	0.828021	−	0.560696i	$-0.189467\pi$
$8$	−1444.01	−	109.551i	−0.997135	−	0.0756489i
$9$		0			0
$10$	−35.6915	+	1413.76i	−0.0112867	+	0.447071i
$11$	−4949.52			−1.12121			−0.560607	−	0.828082i	$-0.689432\pi$
$11$	−4949.52			−1.12121			−0.560607	+	0.828082i	$0.689432\pi$
$12$		0			0
$13$	−5267.74			−0.665001			−0.332500	−	0.943103i	$-0.607892\pi$
$13$	−5267.74			−0.665001			−0.332500	+	0.943103i	$0.607892\pi$
$14$	−290.573	+	11509.8i	−0.0283014	+	1.12104i
$15$		0			0
$16$	16300.6	+	1651.35i	0.994908	+	0.100790i
$17$			21159.8i			1.04458i	0.852769	+	0.522288i	$0.174921\pi$
$17$			21159.8i			1.04458i	−0.852769	+	0.522288i	$0.825079\pi$
$18$		0			0
$19$			12122.1i			0.405454i	0.979235	+	0.202727i	$0.0649804\pi$
$19$			12122.1i			0.405454i	−0.979235	+	0.202727i	$0.935020\pi$
$20$	807.350	−	15979.6i	0.0225661	−	0.446644i
$21$		0			0
$22$	55979.5	+	1413.25i	1.12086	+	0.0282969i
$23$	−10926.7			−0.187258			−0.0936290	−	0.995607i	$-0.529847\pi$
$23$	−10926.7			−0.187258			−0.0936290	+	0.995607i	$0.529847\pi$
$24$		0			0
$25$	−15625.0			−0.200000
$26$	59578.6	+	1504.11i	0.664789	+	0.0167831i
$27$		0			0
$28$	6572.83	−	130094.i	0.0565848	−	1.11996i
$29$			175111.i			1.33328i	0.745381	+	0.666639i	$0.232268\pi$
$29$			175111.i			1.33328i	−0.745381	+	0.666639i	$0.767732\pi$
$30$		0			0
$31$		−	70706.1i		−	0.426276i	−0.977022	−	0.213138i	$-0.931632\pi$
$31$		−	70706.1i		−	0.426276i	0.977022	−	0.213138i	$-0.0683684\pi$
$32$	−183890.	−	23331.2i	−0.992047	−	0.125867i
$33$		0			0
$34$	6041.80	−	239319.i	0.0263627	−	1.04424i
$35$	−127207.			−0.501502
$36$		0			0
$37$	272479.			0.884355			0.442178	−	0.896928i	$-0.354206\pi$
$37$	272479.			0.884355			0.442178	+	0.896928i	$0.354206\pi$
$38$	3461.26	−	137103.i	0.0102327	−	0.405325i
$39$		0			0
$40$	−13693.9	+	180501.i	−0.0338312	+	0.445932i
$41$			23618.7i			0.0535195i	0.999642	+	0.0267598i	$0.00851891\pi$
$41$			23618.7i			0.0535195i	−0.999642	+	0.0267598i	$0.991481\pi$
$42$		0			0
$43$		−	175131.i		−	0.335910i	−0.985795	−	0.167955i	$-0.946284\pi$
$43$		−	175131.i		−	0.335910i	0.985795	−	0.167955i	$-0.0537163\pi$
$44$	−632731.	−	31967.9i	−1.11979	−	0.0565757i
$45$		0			0
$46$	123582.	+	3119.92i	0.187198	+	0.00472596i
$47$	−1.14576e6			−1.60973			−0.804863	−	0.593461i	$-0.797761\pi$
$47$	−1.14576e6			−1.60973			−0.804863	+	0.593461i	$0.797761\pi$
$48$		0			0
$49$	−212080.			−0.257522
$50$	176720.	+	4461.44i	0.199936	+	0.00504754i
$51$		0			0
$52$	−673411.	−	34023.2i	−0.664154	−	0.0335555i
$53$		−	921020.i		−	0.849774i	−0.905246	−	0.424887i	$-0.860314\pi$
$53$		−	921020.i		−	0.849774i	0.905246	−	0.424887i	$-0.139686\pi$
$54$		0			0
$55$			618689.i			0.501422i
$56$	−111485.	+	1.46950e6i	−0.0848321	+	1.11818i
$57$		0			0
$58$	49999.8	−	1.98052e6i	0.0336489	−	1.33285i
$59$	−312509.			−0.198098			−0.0990491	−	0.995083i	$-0.531580\pi$
$59$	−312509.			−0.198098			−0.0990491	+	0.995083i	$0.531580\pi$
$60$		0			0
$61$	581361.			0.327938			0.163969	−	0.986466i	$-0.447570\pi$
$61$	581361.			0.327938			0.163969	+	0.986466i	$0.447570\pi$
$62$	−20188.9	+	799693.i	−0.0107582	+	0.426140i
$63$		0			0
$64$	2.07315e6	+	316385.i	0.988555	+	0.150864i
$65$			658467.i			0.297397i
$66$		0			0
$67$		−	3.05251e6i		−	1.23993i	−0.784631	−	0.619963i	$-0.787148\pi$
$67$		−	3.05251e6i		−	1.23993i	0.784631	−	0.619963i	$-0.212852\pi$
$68$	−136667.	+	2.70500e6i	−0.0527086	+	1.04325i
$69$		0			0
$70$	1.43872e6	+	36321.7i	0.501342	+	0.0126568i
$71$	4.72551e6			1.56691			0.783455	−	0.621448i	$-0.213455\pi$
$71$	4.72551e6			1.56691			0.783455	+	0.621448i	$0.213455\pi$
$72$		0			0
$73$	5.46716e6			1.64487			0.822435	−	0.568860i	$-0.192615\pi$
$73$	5.46716e6			1.64487			0.822435	+	0.568860i	$0.192615\pi$
$74$	−3.08176e6	−	77801.5i	−0.884073	−	0.0223191i
$75$		0			0
$76$	−78294.5	+	1.54966e6i	−0.0204590	+	0.404938i
$77$			5.03690e6i			1.25732i
$78$		0			0
$79$			2.07098e6i			0.472586i	0.971682	+	0.236293i	$0.0759325\pi$
$79$			2.07098e6i			0.472586i	−0.971682	+	0.236293i	$0.924068\pi$
$80$	206418.	−	2.03757e6i	0.0450747	−	0.444936i
$81$		0			0
$82$	6743.89	−	267130.i	0.00135071	−	0.0535025i
$83$	854102.			0.163959			0.0819797	−	0.996634i	$-0.473876\pi$
$83$	854102.			0.163959			0.0819797	+	0.996634i	$0.473876\pi$
$84$		0			0
$85$	2.64497e6			0.467149
$86$	−50005.4	+	1.98075e6i	−0.00847759	+	0.335803i
$87$		0			0
$88$	7.14713e6	+	542226.i	1.11800	+	0.0848185i
$89$			7.69685e6i			1.15731i	0.815574	+	0.578653i	$0.196421\pi$
$89$			7.69685e6i			1.15731i	−0.815574	+	0.578653i	$0.803579\pi$
$90$		0			0
$91$			5.36074e6i			0.745727i
$92$	−1.39683e6	−	70573.2i	−0.187019	−	0.00944892i
$93$		0			0
$94$	1.29587e7	+	327152.i	1.60921	+	0.0406258i
$95$	1.51527e6			0.181325
$96$		0			0
$97$	1.44110e7			1.60322			0.801611	−	0.597846i	$-0.203977\pi$
$97$	1.44110e7			1.60322			0.801611	+	0.597846i	$0.203977\pi$
$98$	2.39865e6	+	60555.7i	0.257440	+	0.00649926i
$99$		0			0
$100$	−1.99745e6	−	100919.i	−0.199745	−	0.0100919i
$101$			1.16399e7i			1.12415i	0.827086	+	0.562075i	$0.189997\pi$
$101$			1.16399e7i			1.12415i	−0.827086	+	0.562075i	$0.810003\pi$
$102$		0			0
$103$			9.09312e6i			0.819941i	0.912099	+	0.409970i	$0.134461\pi$
$103$			9.09312e6i			0.819941i	−0.912099	+	0.409970i	$0.865539\pi$
$104$	7.60664e6	+	577087.i	0.663095	+	0.0503066i
$105$		0			0
$106$	−262981.	+	1.04168e7i	−0.0214464	+	0.849503i
$107$	2.38832e7			1.88473			0.942367	−	0.334581i	$-0.108595\pi$
$107$	2.38832e7			1.88473			0.942367	+	0.334581i	$0.108595\pi$
$108$		0			0
$109$	−1.35844e7			−1.00472			−0.502362	−	0.864658i	$-0.667535\pi$
$109$	−1.35844e7			−1.00472			−0.502362	+	0.864658i	$0.667535\pi$
$110$	176656.	−	6.99744e6i	0.0126547	−	0.501262i
$111$		0			0
$112$	1.68050e6	−	1.65884e7i	0.113025	−	1.11568i
$113$		−	2.42115e7i		−	1.57851i	−0.614067	−	0.789254i	$-0.710467\pi$
$113$		−	2.42115e7i		−	1.57851i	0.614067	−	0.789254i	$-0.289533\pi$
$114$		0			0
$115$			1.36583e6i			0.0837443i
$116$	−1.13101e6	+	2.23857e7i	−0.0672763	+	1.33158i
$117$		0			0
$118$	3.53451e6	+	89231.4i	0.198035	+	0.00499955i
$119$	2.15334e7			1.17138
$120$		0			0
$121$	5.01054e6			0.257120
$122$	−6.57525e6	−	165997.i	−0.327833	−	0.00827640i
$123$		0			0
$124$	456676.	−	9.03885e6i	0.0215096	−	0.425733i
$125$			1.95312e6i			0.0894427i
$126$		0			0
$127$			2.70653e7i			1.17246i	0.810143	+	0.586232i	$0.199389\pi$
$127$			2.70653e7i			1.17246i	−0.810143	+	0.586232i	$0.800611\pi$
$128$	−2.33572e7	−	4.17030e6i	−0.984432	−	0.175765i
$129$		0			0
$130$	188014.	−	7.44733e6i	0.00750563	−	0.297303i
$131$	−1.83771e7			−0.714212			−0.357106	−	0.934064i	$-0.616236\pi$
$131$	−1.83771e7			−0.714212			−0.357106	+	0.934064i	$0.616236\pi$
$132$		0			0
$133$	1.23362e7			0.454673
$134$	−871591.	+	3.45242e7i	−0.0312929	+	1.23953i
$135$		0			0
$136$	2.31808e6	−	3.05548e7i	0.0790210	−	1.04158i
$137$			3.21259e7i			1.06742i	0.845669	+	0.533708i	$0.179202\pi$
$137$			3.21259e7i			1.06742i	−0.845669	+	0.533708i	$0.820798\pi$
$138$		0			0
$139$		−	1.31297e7i		−	0.414670i	−0.978270	−	0.207335i	$-0.933521\pi$
$139$		−	1.31297e7i		−	0.414670i	0.978270	−	0.207335i	$-0.0664790\pi$
$140$	−1.62617e7	−	821604.i	−0.500863	−	0.0253055i
$141$		0			0
$142$	−5.34460e7	−	1.34928e6i	−1.56641	−	0.0395452i
$143$	2.60727e7			0.745608
$144$		0			0
$145$	2.18889e7			0.596260
$146$	−6.18341e7	−	1.56105e6i	−1.64435	−	0.0415127i
$147$		0			0
$148$	3.48329e7	+	1.75989e6i	0.883229	+	0.0446240i
$149$		−	4.50153e7i		−	1.11483i	−0.830234	−	0.557415i	$-0.811793\pi$
$149$		−	4.50153e7i		−	1.11483i	0.830234	−	0.557415i	$-0.188207\pi$
$150$		0			0
$151$			6.23691e7i			1.47418i	0.675795	+	0.737089i	$0.263800\pi$
$151$			6.23691e7i			1.47418i	−0.675795	+	0.737089i	$0.736200\pi$
$152$	1.32800e6	−	1.75044e7i	0.0306721	−	0.404292i
$153$		0			0
$154$	1.43820e6	−	5.69679e7i	0.0317319	−	1.25692i
$155$	−8.83826e6			−0.190636
$156$		0			0
$157$	3.23174e7			0.666481			0.333241	−	0.942842i	$-0.391858\pi$
$157$	3.23174e7			0.666481			0.333241	+	0.942842i	$0.391858\pi$
$158$	591331.	−	2.34230e7i	0.0119270	−	0.472435i
$159$		0			0
$160$	−2.91640e6	+	2.29862e7i	−0.0562895	+	0.443657i
$161$			1.11196e7i			0.209990i
$162$		0			0
$163$		−	9.79963e6i		−	0.177237i	−0.996066	−	0.0886183i	$-0.971755\pi$
$163$		−	9.79963e6i		−	0.177237i	0.996066	−	0.0886183i	$-0.0282451\pi$
$164$	−152548.	+	3.01934e6i	−0.00270056	+	0.0534513i
$165$		0			0
$166$	−9.65998e6	−	243874.i	−0.163907	−	0.00413796i
$167$	4.86412e7			0.808159			0.404080	−	0.914724i	$-0.367592\pi$
$167$	4.86412e7			0.808159			0.404080	+	0.914724i	$0.367592\pi$
$168$		0			0
$169$	−3.49995e7			−0.557774
$170$	−2.99149e7	−	755225.i	−0.467000	−	0.0117898i
$171$		0			0
$172$	1.13113e6	−	2.23882e7i	0.0169498	−	0.335482i
$173$			3.88286e7i			0.570152i	0.958505	+	0.285076i	$0.0920188\pi$
$173$			3.88286e7i			0.570152i	−0.958505	+	0.285076i	$0.907981\pi$
$174$		0			0
$175$			1.59009e7i			0.224279i
$176$	−8.06799e7	−	8.17336e6i	−1.11550	−	0.113007i
$177$		0			0
$178$	2.19770e6	−	8.70522e7i	0.0292077	−	1.15694i
$179$	8.56178e7			1.11578			0.557890	−	0.829915i	$-0.311611\pi$
$179$	8.56178e7			1.11578			0.557890	+	0.829915i	$0.311611\pi$
$180$		0			0
$181$	−1.20518e8			−1.51070			−0.755350	−	0.655322i	$-0.772533\pi$
$181$	−1.20518e8			−1.51070			−0.755350	+	0.655322i	$0.772533\pi$
$182$	1.53066e6	−	6.06305e7i	0.0188205	−	0.745490i
$183$		0			0
$184$	1.57782e7	+	1.19703e6i	0.186721	+	0.0141659i
$185$		−	3.40599e7i		−	0.395496i
$186$		0			0
$187$		−	1.04731e8i		−	1.17119i
$188$	−1.46471e8	−	7.40025e6i	−1.60768	−	0.0812257i
$189$		0			0
$190$	−1.71378e7	−	432658.i	−0.181267	−	0.00457622i
$191$	3.09145e7			0.321029			0.160515	−	0.987033i	$-0.448685\pi$
$191$	3.09145e7			0.321029			0.160515	+	0.987033i	$0.448685\pi$
$192$		0			0
$193$	−1.78880e8			−1.79106			−0.895531	−	0.444998i	$-0.853204\pi$
$193$	−1.78880e8			−1.79106			−0.895531	+	0.444998i	$0.853204\pi$
$194$	−1.62990e8	−	4.11481e6i	−1.60271	−	0.0404616i
$195$		0			0
$196$	−2.71117e7	−	1.36978e6i	−0.257194	−	0.0129944i
$197$		−	9.89610e7i		−	0.922216i	−0.887344	−	0.461108i	$-0.847452\pi$
$197$		−	9.89610e7i		−	0.922216i	0.887344	−	0.461108i	$-0.152548\pi$
$198$		0			0
$199$			1.34679e8i			1.21147i	0.795665	+	0.605736i	$0.207121\pi$
$199$			1.34679e8i			1.21147i	−0.795665	+	0.605736i	$0.792879\pi$
$200$	2.25626e7	+	1.71174e6i	0.199427	+	0.0151298i
$201$		0			0
$202$	3.32356e6	−	1.31648e8i	0.0283710	−	1.12379i
$203$	1.78203e8			1.49513
$204$		0			0
$205$	2.95234e6			0.0239347
$206$	2.59638e6	−	1.02844e8i	0.0206934	−	0.819680i
$207$		0			0
$208$	−8.58671e7	−	8.69885e6i	−0.661615	−	0.0670255i
$209$		−	5.99987e7i		−	0.454601i
$210$		0			0
$211$			2.29710e8i			1.68342i	0.539933	+	0.841708i	$0.318450\pi$
$211$			2.29710e8i			1.68342i	−0.539933	+	0.841708i	$0.681550\pi$
$212$	5.94868e6	−	1.17740e8i	0.0428791	−	0.848692i
$213$		0			0
$214$	−2.70122e8	−	6.81944e6i	−1.88413	−	0.0475664i
$215$	−2.18913e7			−0.150223
$216$		0			0
$217$	−7.19545e7			−0.478023
$218$	1.53641e8	+	3.87877e6i	1.00440	+	0.0253569i
$219$		0			0
$220$	−3.99599e6	+	7.90914e7i	−0.0253014	+	0.500783i
$221$		−	1.11464e8i		−	0.694644i
$222$		0			0
$223$			1.62401e8i			0.980670i	0.871534	+	0.490335i	$0.163125\pi$
$223$			1.62401e8i			0.980670i	−0.871534	+	0.490335i	$0.836875\pi$
$224$	−2.37432e7	+	1.87136e8i	−0.141147	+	1.11247i
$225$		0			0
$226$	−6.91316e6	+	2.73834e8i	−0.0398380	+	1.57801i
$227$	2.61737e8			1.48516			0.742582	−	0.669755i	$-0.233601\pi$
$227$	2.61737e8			1.48516			0.742582	+	0.669755i	$0.233601\pi$
$228$		0			0
$229$	−2.45757e7			−0.135233			−0.0676164	−	0.997711i	$-0.521539\pi$
$229$	−2.45757e7			−0.135233			−0.0676164	+	0.997711i	$0.521539\pi$
$230$	389990.	−	1.54477e7i	0.00211352	−	0.0837177i
$231$		0			0
$232$	1.91836e7	−	2.52861e8i	0.100861	−	1.32946i
$233$			3.76804e7i			0.195151i	0.995228	+	0.0975754i	$0.0311087\pi$
$233$			3.76804e7i			0.195151i	−0.995228	+	0.0975754i	$0.968891\pi$
$234$		0			0
$235$			1.43220e8i			0.719891i
$236$	−3.99502e7	−	2.01843e6i	−0.197846	−	0.00999591i
$237$		0			0
$238$	−2.43545e8	−	6.14847e6i	−1.17101	−	0.0295630i
$239$	1.58923e8			0.752999			0.376500	−	0.926417i	$-0.377128\pi$
$239$	1.58923e8			0.752999			0.376500	+	0.926417i	$0.377128\pi$
$240$		0			0
$241$	3.45238e8			1.58876			0.794381	−	0.607420i	$-0.207796\pi$
$241$	3.45238e8			1.58876			0.794381	+	0.607420i	$0.207796\pi$
$242$	−5.66697e7	−	1.43067e6i	−0.257038	−	0.00648912i
$243$		0			0
$244$	7.43194e7	+	3.75489e6i	0.327520	+	0.0165475i
$245$			2.65100e7i			0.115167i
$246$		0			0
$247$		−	6.38562e7i		−	0.269627i
$248$	−7.74594e6	+	1.02100e8i	−0.0322473	+	0.425055i
$249$		0			0
$250$	557680.	−	2.20900e7i	0.00225733	−	0.0894142i
$251$	1.30430e8			0.520617			0.260309	−	0.965525i	$-0.416176\pi$
$251$	1.30430e8			0.520617			0.260309	+	0.965525i	$0.416176\pi$
$252$		0			0
$253$	5.40817e7			0.209956
$254$	7.72801e6	−	3.06111e8i	0.0295903	−	1.17209i
$255$		0			0
$256$	2.62982e8	+	5.38358e7i	0.979683	+	0.200554i
$257$		−	4.75395e8i		−	1.74698i	−0.486838	−	0.873492i	$-0.661850\pi$
$257$		−	4.75395e8i		−	1.74698i	0.486838	−	0.873492i	$-0.338150\pi$
$258$		0			0
$259$		−	2.77290e8i		−	0.991709i
$260$	−4.25291e6	+	8.41764e7i	−0.0150065	+	0.297019i
$261$		0			0
$262$	2.07847e8	+	5.24725e6i	0.713984	+	0.0180251i
$263$	−1.50093e8			−0.508763			−0.254382	−	0.967104i	$-0.581872\pi$
$263$	−1.50093e8			−0.508763			−0.254382	+	0.967104i	$0.581872\pi$
$264$		0			0
$265$	−1.15127e8			−0.380031
$266$	−1.39523e8	−	3.52237e6i	−0.454528	−	0.0114749i
$267$		0			0
$268$	1.97156e7	−	3.90224e8i	0.0625659	−	1.23835i
$269$			5.82841e8i			1.82565i	0.408351	+	0.912825i	$0.366104\pi$
$269$			5.82841e8i			1.82565i	−0.408351	+	0.912825i	$0.633896\pi$
$270$		0			0
$271$			4.19542e8i			1.28051i	0.768162	+	0.640256i	$0.221172\pi$
$271$			4.19542e8i			1.28051i	−0.768162	+	0.640256i	$0.778828\pi$
$272$	−3.49421e7	+	3.44917e8i	−0.105283	+	1.03926i
$273$		0			0
$274$	9.17298e6	−	3.63347e8i	0.0269391	−	1.06708i
$275$	7.73362e7			0.224243
$276$		0			0
$277$	3.76239e7			0.106361			0.0531807	−	0.998585i	$-0.483064\pi$
$277$	3.76239e7			0.106361			0.0531807	+	0.998585i	$0.483064\pi$
$278$	−3.74895e6	+	1.48498e8i	−0.0104653	+	0.414538i
$279$		0			0
$280$	1.83687e8	+	1.39357e7i	0.500065	+	0.0379381i
$281$		−	3.71855e7i		−	0.0999774i	−0.998750	−	0.0499887i	$-0.984081\pi$
$281$		−	3.71855e7i		−	0.0999774i	0.998750	−	0.0499887i	$-0.0159185\pi$
$282$		0			0
$283$			9.73301e7i			0.255267i	0.991821	+	0.127633i	$0.0407381\pi$
$283$			9.73301e7i			0.255267i	−0.991821	+	0.127633i	$0.959262\pi$
$284$	6.04094e8	+	3.05211e7i	1.56491	+	0.0790653i
$285$		0			0
$286$	−2.94885e8	−	7.44461e6i	−0.745371	−	0.0188174i
$287$	2.40357e7			0.0600164
$288$		0			0
$289$	−3.73978e7			−0.0911389
$290$	−2.47565e8	−	6.24998e6i	−0.596070	−	0.0150482i
$291$		0			0
$292$	6.98904e8	+	3.53113e7i	1.64277	+	0.0829991i
$293$			6.46069e8i			1.50052i	0.661142	+	0.750261i	$0.270072\pi$
$293$			6.46069e8i			1.50052i	−0.661142	+	0.750261i	$0.729928\pi$
$294$		0			0
$295$			3.90636e7i			0.0885922i
$296$	−3.93461e8	−	2.98504e7i	−0.881821	−	0.0669005i
$297$		0			0
$298$	−1.28533e7	+	5.09128e8i	−0.0281358	+	1.11447i
$299$	5.75588e7			0.124527
$300$		0			0
$301$	−1.78223e8			−0.376687
$302$	1.78084e7	−	7.05401e8i	0.0372049	−	1.47371i
$303$		0			0
$304$	−2.00178e7	+	1.97598e8i	−0.0408658	+	0.403389i
$305$		−	7.26701e7i		−	0.146658i
$306$		0			0
$307$		−	1.77114e8i		−	0.349357i	−0.984626	−	0.174678i	$-0.944111\pi$
$307$		−	1.77114e8i		−	0.349357i	0.984626	−	0.174678i	$-0.0558885\pi$
$308$	−3.25323e7	+	6.43902e8i	−0.0634436	+	1.25572i
$309$		0			0
$310$	9.99617e7	+	2.52361e6i	0.190576	+	0.00481123i
$311$	−9.69334e8			−1.82731			−0.913655	−	0.406490i	$-0.866753\pi$
$311$	−9.69334e8			−1.82731			−0.913655	+	0.406490i	$0.866753\pi$
$312$		0			0
$313$	4.07689e8			0.751491			0.375746	−	0.926723i	$-0.377387\pi$
$313$	4.07689e8			0.751491			0.375746	+	0.926723i	$0.377387\pi$
$314$	−3.65513e8	−	9.22766e6i	−0.666269	−	0.0168205i
$315$		0			0
$316$	−1.33760e7	+	2.64747e8i	−0.0238464	+	0.471984i
$317$		−	4.14374e8i		−	0.730609i	−0.930888	−	0.365304i	$-0.880965\pi$
$317$		−	4.14374e8i		−	0.730609i	0.930888	−	0.365304i	$-0.119035\pi$
$318$		0			0
$319$		−	8.66715e8i		−	1.49489i
$320$	3.95481e7	−	2.59144e8i	0.0674685	−	0.442095i
$321$		0			0
$322$	3.17500e6	−	1.25764e8i	0.00529966	−	0.209923i
$323$	−2.56502e8			−0.423528
$324$		0			0
$325$	8.23084e7			0.133000
$326$	−2.79811e6	+	1.10835e8i	−0.00447305	+	0.177180i
$327$		0			0
$328$	2.58746e6	−	3.41055e7i	0.00404869	−	0.0533662i
$329$			1.16599e9i			1.80514i
$330$		0			0
$331$		−	5.42363e8i		−	0.822038i	−0.911627	−	0.411019i	$-0.865173\pi$
$331$		−	5.42363e8i		−	0.822038i	0.911627	−	0.411019i	$-0.134827\pi$
$332$	1.09186e8	+	5.51647e6i	0.163751	+	0.00827329i
$333$		0			0
$334$	−5.50138e8	−	1.38886e7i	−0.807902	−	0.0203961i
$335$	−3.81564e8			−0.554512
$336$		0			0
$337$	6.68411e8			0.951347			0.475674	−	0.879622i	$-0.342204\pi$
$337$	6.68411e8			0.951347			0.475674	+	0.879622i	$0.342204\pi$
$338$	3.95848e8	+	9.99348e6i	0.557596	+	0.0140769i
$339$		0			0
$340$	3.38125e8	+	1.70833e7i	0.466553	+	0.0235720i
$341$			3.49961e8i			0.477946i
$342$		0			0
$343$		−	6.22259e8i		−	0.832610i
$344$	−1.91858e7	+	2.52889e8i	−0.0254112	+	0.334947i
$345$		0			0
$346$	1.10868e7	−	4.39156e8i	0.0143893	−	0.569970i
$347$	−2.60027e8			−0.334091			−0.167045	−	0.985949i	$-0.553423\pi$
$347$	−2.60027e8			−0.334091			−0.167045	+	0.985949i	$0.553423\pi$
$348$		0			0
$349$	2.22935e8			0.280731			0.140365	−	0.990100i	$-0.455172\pi$
$349$	2.22935e8			0.280731			0.140365	+	0.990100i	$0.455172\pi$
$350$	4.54021e6	−	1.79841e8i	0.00566028	−	0.224207i
$351$		0			0
$352$	9.10165e8	+	1.15478e8i	1.11230	+	0.141124i
$353$		−	4.51937e8i		−	0.546848i	−0.961894	−	0.273424i	$-0.911844\pi$
$353$		−	4.51937e8i		−	0.546848i	0.961894	−	0.273424i	$-0.0881561\pi$
$354$		0			0
$355$		−	5.90688e8i		−	0.700744i
$356$	−4.97124e7	+	9.83942e8i	−0.0583969	+	1.15583i
$357$		0			0
$358$	−9.68346e8	−	2.44466e7i	−1.11542	−	0.0281597i
$359$	1.68222e8			0.191890			0.0959451	−	0.995387i	$-0.469413\pi$
$359$	1.68222e8			0.191890			0.0959451	+	0.995387i	$0.469413\pi$
$360$		0			0
$361$	7.46925e8			0.835607
$362$	1.36307e9	+	3.44119e7i	1.51022	+	0.0381266i
$363$		0			0
$364$	−3.46239e7	+	6.85301e8i	−0.0376289	+	0.744777i
$365$		−	6.83394e8i		−	0.735608i
$366$		0			0
$367$		−	3.78483e8i		−	0.399682i	−0.979828	−	0.199841i	$-0.935957\pi$
$367$		−	3.78483e8i		−	0.399682i	0.979828	−	0.199841i	$-0.0640426\pi$
$368$	−1.78111e8	−	1.80437e7i	−0.186304	−	0.0188738i
$369$		0			0
$370$	−9.72518e6	+	3.85220e8i	−0.00998141	+	0.395370i
$371$	−9.37281e8			−0.952931
$372$		0			0
$373$	−1.71049e8			−0.170663			−0.0853314	−	0.996353i	$-0.527195\pi$
$373$	−1.71049e8			−0.170663			−0.0853314	+	0.996353i	$0.527195\pi$
$374$	−2.99040e7	+	1.18452e9i	−0.0295582	+	1.17082i
$375$		0			0
$376$	1.65449e9	+	1.25520e8i	1.60511	+	0.121774i
$377$		−	9.22439e8i		−	0.886631i
$378$		0			0
$379$			1.39453e9i			1.31580i	0.753106	+	0.657899i	$0.228555\pi$
$379$			1.39453e9i			1.31580i	−0.753106	+	0.657899i	$0.771445\pi$
$380$	1.93707e8	+	9.78681e6i	0.181094	+	0.00914952i
$381$		0			0
$382$	−3.49646e8	−	8.82707e6i	−0.320927	−	0.00810205i
$383$	−2.07864e8			−0.189053			−0.0945266	−	0.995522i	$-0.530134\pi$
$383$	−2.07864e8			−0.189053			−0.0945266	+	0.995522i	$0.530134\pi$
$384$		0			0
$385$	6.29613e8			0.562291
$386$	2.02315e9	+	5.10760e7i	1.79049	+	0.0452023i
$387$		0			0
$388$	1.84226e9	+	9.30778e7i	1.60118	+	0.0808975i
$389$			1.61926e7i			0.0139474i	0.999976	+	0.00697370i	$0.00221982\pi$
$389$			1.61926e7i			0.0139474i	−0.999976	+	0.00697370i	$0.997780\pi$
$390$		0			0
$391$		−	2.31206e8i		−	0.195605i
$392$	3.06245e8	+	2.32336e7i	0.256784	+	0.0194812i
$393$		0			0
$394$	−2.82566e7	+	1.11926e9i	−0.0232746	+	0.921922i
$395$	2.58872e8			0.211347
$396$		0			0
$397$	1.11223e9			0.892127			0.446063	−	0.895001i	$-0.352826\pi$
$397$	1.11223e9			0.892127			0.446063	+	0.895001i	$0.352826\pi$
$398$	3.84551e7	−	1.52323e9i	0.0305748	−	1.21109i
$399$		0			0
$400$	−2.54696e8	−	2.58023e7i	−0.198982	−	0.0201580i
$401$			1.62678e9i			1.25986i	0.776651	+	0.629931i	$0.216917\pi$
$401$			1.62678e9i			1.25986i	−0.776651	+	0.629931i	$0.783083\pi$
$402$		0			0
$403$			3.72461e8i			0.283474i
$404$	−7.51797e7	+	1.48801e9i	−0.0567239	+	1.12272i
$405$		0			0
$406$	−2.01549e9	−	5.08826e7i	−1.49465	−	0.0377336i
$407$	−1.34864e9			−0.991551
$408$		0			0
$409$	−1.90820e9			−1.37909			−0.689543	−	0.724245i	$-0.742189\pi$
$409$	−1.90820e9			−1.37909			−0.689543	+	0.724245i	$0.742189\pi$
$410$	−3.33912e7	−	842987.i	−0.0239270	−	0.000604056i
$411$		0			0
$412$	−5.87306e7	+	1.16244e9i	−0.0413737	+	0.818896i
$413$			3.18027e8i			0.222146i
$414$		0			0
$415$		−	1.06763e8i		−	0.0733249i
$416$	9.68682e8	+	1.22903e8i	0.659712	+	0.0837018i
$417$		0			0
$418$	−1.71316e7	+	6.78592e8i	−0.0114731	+	0.454456i
$419$	−1.79661e9			−1.19318			−0.596589	−	0.802547i	$-0.703478\pi$
$419$	−1.79661e9			−1.19318			−0.596589	+	0.802547i	$0.703478\pi$
$420$		0			0
$421$	−2.68101e9			−1.75110			−0.875551	−	0.483126i	$-0.839501\pi$
$421$	−2.68101e9			−1.75110			−0.875551	+	0.483126i	$0.839501\pi$
$422$	6.55896e7	−	2.59805e9i	0.0424856	−	1.68288i
$423$		0			0
$424$	−1.00899e8	+	1.32996e9i	−0.0642844	+	0.847339i
$425$		−	3.30622e8i		−	0.208915i
$426$		0			0
$427$		−	5.91625e8i		−	0.367747i
$428$	3.05316e9	+	1.54257e8i	1.88233	+	0.0951025i
$429$		0			0
$430$	2.47593e8	+	6.25068e6i	0.150175	+	0.00379129i
$431$	2.39915e9			1.44340			0.721699	−	0.692207i	$-0.243361\pi$
$431$	2.39915e9			1.44340			0.721699	+	0.692207i	$0.243361\pi$
$432$		0			0
$433$	−1.23124e9			−0.728844			−0.364422	−	0.931234i	$-0.618733\pi$
$433$	−1.23124e9			−0.728844			−0.364422	+	0.931234i	$0.618733\pi$
$434$	8.13812e8	+	2.05453e7i	0.477871	+	0.0120642i
$435$		0			0
$436$	−1.73658e9	−	8.77387e7i	−1.00344	−	0.0506977i
$437$		−	1.32455e8i		−	0.0759245i
$438$		0			0
$439$		−	2.36789e9i		−	1.33578i	−0.744258	−	0.667892i	$-0.767197\pi$
$439$		−	2.36789e9i		−	1.33578i	0.744258	−	0.667892i	$-0.232803\pi$
$440$	6.77782e7	−	8.93391e8i	0.0379320	−	0.499985i
$441$		0			0
$442$	−3.18266e7	+	1.26067e9i	−0.0175312	+	0.694423i
$443$	−1.98826e9			−1.08657			−0.543287	−	0.839547i	$-0.682821\pi$
$443$	−1.98826e9			−1.08657			−0.543287	+	0.839547i	$0.682821\pi$
$444$		0			0
$445$	9.62106e8			0.517563
$446$	4.63708e7	−	1.83678e9i	0.0247499	−	0.980357i
$447$		0			0
$448$	3.21971e8	−	2.10975e9i	0.169178	−	1.10856i
$449$		−	2.58417e8i		−	0.134729i	−0.997728	−	0.0673643i	$-0.978541\pi$
$449$		−	2.58417e8i		−	0.134729i	0.997728	−	0.0673643i	$-0.0214590\pi$
$450$		0			0
$451$		−	1.16901e8i		−	0.0600068i
$452$	1.56377e8	−	3.09512e9i	0.0796505	−	1.57650i
$453$		0			0
$454$	−2.96027e9	−	7.47344e7i	−1.48469	−	0.0374822i
$455$	6.70093e8			0.333499
$456$		0			0
$457$	1.02477e9			0.502252			0.251126	−	0.967954i	$-0.419199\pi$
$457$	1.02477e9			0.502252			0.251126	+	0.967954i	$0.419199\pi$
$458$	2.77954e8	+	7.01716e6i	0.135190	+	0.00341297i
$459$		0			0
$460$	−8.82164e6	+	1.74604e8i	−0.00422569	+	0.0836376i
$461$		−	1.66082e9i		−	0.789531i	−0.918782	−	0.394765i	$-0.870826\pi$
$461$		−	1.66082e9i		−	0.789531i	0.918782	−	0.394765i	$-0.129174\pi$
$462$		0			0
$463$			1.33523e8i			0.0625205i	0.999511	+	0.0312602i	$0.00995206\pi$
$463$			1.33523e8i			0.0625205i	−0.999511	+	0.0312602i	$0.990048\pi$
$464$	−2.89169e8	+	2.85441e9i	−0.134381	+	1.32649i
$465$		0			0
$466$	1.07590e7	−	4.26170e8i	0.00492516	−	0.195089i
$467$	−3.45042e9			−1.56770			−0.783851	−	0.620949i	$-0.786747\pi$
$467$	−3.45042e9			−1.56770			−0.783851	+	0.620949i	$0.786747\pi$
$468$		0			0
$469$	−3.10641e9			−1.39044
$470$	4.08940e7	−	1.61984e9i	0.0181684	−	0.719662i
$471$		0			0
$472$	4.51265e8	+	3.42357e7i	0.197531	+	0.0149859i
$473$			8.66812e8i			0.376626i
$474$		0			0
$475$		−	1.89408e8i		−	0.0810908i
$476$	2.75276e9	+	1.39080e8i	1.16989	+	0.0591071i
$477$		0			0
$478$	−1.79744e9	−	4.53777e7i	−0.752759	−	0.0190040i
$479$	1.18595e9			0.493052			0.246526	−	0.969136i	$-0.420711\pi$
$479$	1.18595e9			0.493052			0.246526	+	0.969136i	$0.420711\pi$
$480$		0			0
$481$	−1.43535e9			−0.588097
$482$	−3.90468e9	−	9.85765e7i	−1.58826	−	0.0400967i
$483$		0			0
$484$	6.40532e8	+	3.23620e7i	0.256792	+	0.0129741i
$485$		−	1.80138e9i		−	0.716982i
$486$		0			0
$487$			4.27332e9i			1.67654i	0.545256	+	0.838270i	$0.316432\pi$
$487$			4.27332e9i			1.67654i	−0.545256	+	0.838270i	$0.683568\pi$
$488$	−8.39488e8	−	6.36888e7i	−0.326998	−	0.0248081i
$489$		0			0
$490$	7.56946e6	−	2.99831e8i	0.00290656	−	0.115131i
$491$	−2.38152e8			−0.0907965			−0.0453982	−	0.998969i	$-0.514456\pi$
$491$	−2.38152e8			−0.0907965			−0.0453982	+	0.998969i	$0.514456\pi$
$492$		0			0
$493$	−3.70531e9			−1.39271
$494$	−1.82330e7	+	7.22221e8i	−0.00680478	+	0.269541i
$495$		0			0
$496$	1.16760e8	−	1.15255e9i	0.0429644	−	0.424105i
$497$		−	4.80894e9i		−	1.75712i
$498$		0			0
$499$		−	4.03075e9i		−	1.45222i	−0.687577	−	0.726112i	$-0.741325\pi$
$499$		−	4.03075e9i		−	1.45222i	0.687577	−	0.726112i	$-0.258675\pi$
$500$	−1.26148e7	+	2.49682e8i	−0.00451322	+	0.0893288i
$501$		0			0
$502$	−1.47517e9	−	3.72419e7i	−0.520452	−	0.0131392i
$503$	−2.94575e9			−1.03207			−0.516033	−	0.856569i	$-0.672592\pi$
$503$	−2.94575e9			−1.03207			−0.516033	+	0.856569i	$0.672592\pi$
$504$		0			0
$505$	1.45499e9			0.502735
$506$	−6.11670e8	−	1.54421e7i	−0.209889	−	0.00529882i
$507$		0			0
$508$	−1.74809e8	+	3.45994e9i	−0.0591618	+	1.17097i
$509$			1.01634e9i			0.341607i	0.985305	+	0.170804i	$0.0546364\pi$
$509$			1.01634e9i			0.341607i	−0.985305	+	0.170804i	$0.945364\pi$
$510$		0			0
$511$		−	5.56368e9i		−	1.84454i
$512$	−2.95898e9	−	6.83978e8i	−0.974309	−	0.225215i
$513$		0			0
$514$	−1.35741e8	+	5.37677e9i	−0.0440899	+	1.74643i
$515$	1.13664e9			0.366689
$516$		0			0
$517$	5.67097e9			1.80485
$518$	−7.91751e7	+	3.13617e9i	−0.0250285	+	0.991394i
$519$		0			0
$520$	7.21359e7	−	9.50830e8i	0.0224978	−	0.296545i
$521$		−	6.78205e7i		−	0.0210101i	−0.999945	−	0.0105051i	$-0.996656\pi$
$521$		−	6.78205e7i		−	0.0210101i	0.999945	−	0.0105051i	$-0.00334393\pi$
$522$		0			0
$523$			4.64218e9i			1.41895i	0.704732	+	0.709473i	$0.251067\pi$
$523$			4.64218e9i			1.41895i	−0.704732	+	0.709473i	$0.748933\pi$
$524$	−2.34927e9	−	1.18694e8i	−0.713302	−	0.0360387i
$525$		0			0
$526$	1.69757e9	+	4.28564e7i	0.508601	+	0.0128400i
$527$	1.49613e9			0.445278
$528$		0			0
$529$	−3.28543e9			−0.964934
$530$	1.30210e9	+	3.28726e7i	0.379909	+	0.00959110i
$531$		0			0
$532$	1.57702e9	+	7.96768e7i	0.454094	+	0.0229425i
$533$		−	1.24417e8i		−	0.0355905i
$534$		0			0
$535$		−	2.98541e9i		−	0.842879i
$536$	−3.34407e8	+	4.40784e9i	−0.0937990	+	1.23637i
$537$		0			0
$538$	1.66420e8	−	6.59200e9i	0.0460752	−	1.82507i
$539$	1.04969e9			0.288737
$540$		0			0
$541$	3.11789e9			0.846585			0.423293	−	0.905993i	$-0.360874\pi$
$541$	3.11789e9			0.846585			0.423293	+	0.905993i	$0.360874\pi$
$542$	1.19793e8	−	4.74507e9i	0.0323172	−	1.28010i
$543$		0			0
$544$	4.93684e8	−	3.89106e9i	0.131478	−	1.03627i
$545$			1.69805e9i			0.449326i
$546$		0			0
$547$		−	2.06605e9i		−	0.539741i	−0.962897	−	0.269870i	$-0.913019\pi$
$547$		−	2.06605e9i		−	0.539741i	0.962897	−	0.269870i	$-0.0869808\pi$
$548$	−2.07495e8	+	4.10688e9i	−0.0538611	+	1.06606i
$549$		0			0
$550$	−8.74680e8	−	2.20820e7i	−0.224171	−	0.00565937i
$551$	−2.12272e9			−0.540583
$552$		0			0
$553$	2.10754e9			0.529954
$554$	−4.25530e8	−	1.07428e7i	−0.106328	−	0.00268432i
$555$		0			0
$556$	8.48020e7	−	1.67846e9i	0.0209240	−	0.414142i
$557$		−	1.35591e9i		−	0.332458i	−0.986087	−	0.166229i	$-0.946841\pi$
$557$		−	1.35591e9i		−	0.332458i	0.986087	−	0.166229i	$-0.0531591\pi$
$558$		0			0
$559$			9.22542e8i			0.223380i
$560$	−2.07355e9	−	2.10063e8i	−0.498948	−	0.0505465i
$561$		0			0
$562$	−1.06177e7	+	4.20572e8i	−0.00252320	+	0.0999456i
$563$	−1.03728e9			−0.244973			−0.122486	−	0.992470i	$-0.539087\pi$
$563$	−1.03728e9			−0.244973			−0.122486	+	0.992470i	$0.539087\pi$
$564$		0			0
$565$	−3.02644e9			−0.705930
$566$	2.77909e7	−	1.10081e9i	0.00644235	−	0.255186i
$567$		0			0
$568$	−6.82365e9	−	5.17685e8i	−1.56242	−	0.118535i
$569$			7.80253e9i			1.77559i	0.460239	+	0.887795i	$0.347764\pi$
$569$			7.80253e9i			1.77559i	−0.460239	+	0.887795i	$0.652236\pi$
$570$		0			0
$571$			3.86907e9i			0.869721i	0.900498	+	0.434860i	$0.143202\pi$
$571$			3.86907e9i			0.869721i	−0.900498	+	0.434860i	$0.856798\pi$
$572$	3.33306e9	+	1.68399e8i	0.744658	+	0.0376229i
$573$		0			0
$574$	−2.71846e8	−	6.86296e6i	−0.0599973	−	0.00151468i
$575$	1.70729e8			0.0374516
$576$		0			0
$577$	5.91115e8			0.128102			0.0640511	−	0.997947i	$-0.479598\pi$
$577$	5.91115e8			0.128102			0.0640511	+	0.997947i	$0.479598\pi$
$578$	4.22973e8	+	1.06783e7i	0.0911099	+	0.00230014i
$579$		0			0
$580$	2.79821e9	+	1.41376e8i	0.595500	+	0.0300869i
$581$		−	8.69182e8i		−	0.183863i
$582$		0			0
$583$			4.55860e9i			0.952778i
$584$	−7.89460e9	−	5.98934e8i	−1.64016	−	0.124432i
$585$		0			0
$586$	1.84474e8	−	7.30711e9i	0.0378698	−	1.50004i
$587$	2.86809e9			0.585274			0.292637	−	0.956224i	$-0.405467\pi$
$587$	2.86809e9			0.585274			0.292637	+	0.956224i	$0.405467\pi$
$588$		0			0
$589$	8.57109e8			0.172835
$590$	1.11539e7	−	4.41814e8i	0.00223586	−	0.0885640i
$591$		0			0
$592$	4.44156e9	+	4.49957e8i	0.879852	+	0.0891343i
$593$			3.55302e9i			0.699692i	0.936807	+	0.349846i	$0.113766\pi$
$593$			3.55302e9i			0.699692i	−0.936807	+	0.349846i	$0.886234\pi$
$594$		0			0
$595$		−	2.69167e9i		−	0.523857i
$596$	2.90745e8	−	5.75462e9i	0.0562536	−	1.11341i
$597$		0			0
$598$	−6.50996e8	−	1.64349e7i	−0.124487	−	0.00314277i
$599$	9.03993e9			1.71859			0.859293	−	0.511484i	$-0.170904\pi$
$599$	9.03993e9			1.71859			0.859293	+	0.511484i	$0.170904\pi$
$600$		0			0
$601$	2.36563e9			0.444515			0.222257	−	0.974988i	$-0.428657\pi$
$601$	2.36563e9			0.444515			0.222257	+	0.974988i	$0.428657\pi$
$602$	2.01572e9	+	5.08883e7i	0.376567	+	0.00950671i
$603$		0			0
$604$	−4.02829e8	+	7.97307e9i	−0.0743861	+	1.47230i
$605$		−	6.26317e8i		−	0.114987i
$606$		0			0
$607$			8.45762e9i			1.53493i	0.641092	+	0.767464i	$0.278482\pi$
$607$			8.45762e9i			1.53493i	−0.641092	+	0.767464i	$0.721518\pi$
$608$	2.82824e8	−	2.22914e9i	0.0510334	−	0.402230i
$609$		0			0
$610$	−2.07496e7	+	8.21906e8i	−0.00370132	+	0.146611i
$611$	6.03557e9			1.07047
$612$		0			0
$613$	−6.25354e8			−0.109652			−0.0548258	−	0.998496i	$-0.517460\pi$
$613$	−6.25354e8			−0.109652			−0.0548258	+	0.998496i	$0.517460\pi$
$614$	−5.05718e7	+	2.00318e9i	−0.00881696	+	0.349245i
$615$		0			0
$616$	5.51799e8	−	7.27331e9i	0.0951149	−	1.25372i
$617$		−	3.02077e9i		−	0.517749i	−0.965911	−	0.258874i	$-0.916648\pi$
$617$		−	3.02077e9i		−	0.517749i	0.965911	−	0.258874i	$-0.0833516\pi$
$618$		0			0
$619$			6.17230e9i			1.04600i	0.852334	+	0.522998i	$0.175186\pi$
$619$			6.17230e9i			1.04600i	−0.852334	+	0.522998i	$0.824814\pi$
$620$	−1.12986e9	−	5.70845e7i	−0.190394	−	0.00961939i
$621$		0			0
$622$	1.09633e10	+	2.76776e8i	1.82673	+	0.0461171i
$623$	7.83274e9			1.29779
$624$		0			0
$625$	2.44141e8			0.0400000
$626$	−4.61101e9	−	1.16408e8i	−0.751252	−	0.0189659i
$627$		0			0
$628$	4.13136e9	+	2.08732e8i	0.665632	+	0.0336302i
$629$			5.76559e9i			0.923776i
$630$		0			0
$631$			4.87433e9i			0.772346i	0.922426	+	0.386173i	$0.126203\pi$
$631$			4.87433e9i			0.772346i	−0.922426	+	0.386173i	$0.873797\pi$
$632$	2.26878e8	−	2.99050e9i	0.0357506	−	0.471232i
$633$		0			0
$634$	−1.18317e8	+	4.68661e9i	−0.0184389	+	0.730376i
$635$	3.38316e9			0.524342
$636$		0			0
$637$	1.11718e9			0.171252
$638$	−2.47475e8	+	9.80263e9i	−0.0377276	+	1.49441i
$639$		0			0
$640$	−5.21287e8	+	2.91965e9i	−0.0786045	+	0.440251i
$641$		−	4.89061e9i		−	0.733433i	−0.930333	−	0.366716i	$-0.880482\pi$
$641$		−	4.89061e9i		−	0.733433i	0.930333	−	0.366716i	$-0.119518\pi$
$642$		0			0
$643$			6.10990e9i			0.906349i	0.891422	+	0.453175i	$0.149709\pi$
$643$			6.10990e9i			0.906349i	−0.891422	+	0.453175i	$0.850291\pi$
$644$	−7.18192e7	+	1.42149e9i	−0.0105959	+	0.209722i
$645$		0			0
$646$	2.90106e9	+	7.32395e7i	0.423393	+	0.0106889i
$647$	−3.73607e9			−0.542313			−0.271156	−	0.962535i	$-0.587406\pi$
$647$	−3.73607e9			−0.542313			−0.271156	+	0.962535i	$0.587406\pi$
$648$		0			0
$649$	1.54677e9			0.222110
$650$	−9.30916e8	−	2.35017e7i	−0.132958	−	0.00335662i
$651$		0			0
$652$	6.32939e7	−	1.25276e9i	0.00894324	−	0.177011i
$653$			8.74159e9i			1.22855i	0.789090	+	0.614277i	$0.210552\pi$
$653$			8.74159e9i			1.22855i	−0.789090	+	0.614277i	$0.789448\pi$
$654$		0			0
$655$			2.29714e9i			0.319405i
$656$	−3.90026e7	+	3.84998e8i	−0.00539424	+	0.0532470i
$657$		0			0
$658$	3.32928e8	−	1.31875e10i	0.0455575	−	1.80456i
$659$	9.06167e9			1.23342			0.616708	−	0.787192i	$-0.288466\pi$
$659$	9.06167e9			1.23342			0.616708	+	0.787192i	$0.288466\pi$
$660$		0			0
$661$	5.60960e8			0.0755486			0.0377743	−	0.999286i	$-0.487973\pi$
$661$	5.60960e8			0.0755486			0.0377743	+	0.999286i	$0.487973\pi$
$662$	−1.54862e8	+	6.13418e9i	−0.0207464	+	0.821776i
$663$		0			0
$664$	−1.23333e9	−	9.35679e7i	−0.163490	−	0.0124033i
$665$		−	1.54202e9i		−	0.203336i
$666$		0			0
$667$		−	1.91338e9i		−	0.249667i
$668$	6.21815e9	+	3.14164e8i	0.807130	+	0.0407792i
$669$		0			0
$670$	4.31553e9	+	1.08949e8i	0.554335	+	0.0139946i
$671$	−2.87745e9			−0.367688
$672$		0			0
$673$	8.09503e9			1.02368			0.511842	−	0.859080i	$-0.328963\pi$
$673$	8.09503e9			1.02368			0.511842	+	0.859080i	$0.328963\pi$
$674$	−7.55980e9	−	1.90853e8i	−0.951044	−	0.0240098i
$675$		0			0
$676$	−4.47423e9	−	2.26055e8i	−0.557063	−	0.0281449i
$677$		−	1.44490e10i		−	1.78968i	−0.446382	−	0.894842i	$-0.647288\pi$
$677$		−	1.44490e10i		−	1.78968i	0.446382	−	0.894842i	$-0.352712\pi$
$678$		0			0
$679$		−	1.46655e10i		−	1.79784i
$680$	−3.81935e9	−	2.89760e8i	−0.465810	−	0.0353393i
$681$		0			0
$682$	9.99251e7	−	3.95809e9i	0.0120623	−	0.477794i
$683$	2.15387e9			0.258671			0.129336	−	0.991601i	$-0.458716\pi$
$683$	2.15387e9			0.258671			0.129336	+	0.991601i	$0.458716\pi$
$684$		0			0
$685$	4.01574e9			0.477363
$686$	−1.77675e8	+	7.03781e9i	−0.0210132	+	0.832345i
$687$		0			0
$688$	2.89201e8	−	2.85473e9i	0.0338564	−	0.334199i
$689$			4.85169e9i			0.565101i
$690$		0			0
$691$			1.09453e10i			1.26199i	0.775788	+	0.630993i	$0.217353\pi$
$691$			1.09453e10i			1.26199i	−0.775788	+	0.630993i	$0.782647\pi$
$692$	−2.50786e8	+	4.96373e9i	−0.0287695	+	0.569426i
$693$		0			0
$694$	2.94093e9	+	7.42460e7i	0.333985	+	0.00843169i
$695$	−1.64121e9			−0.185446
$696$		0			0
$697$	−4.99766e8			−0.0559052
$698$	−2.52142e9	−	6.36552e7i	−0.280641	−	0.00708500i
$699$		0			0
$700$	−1.02701e8	+	2.03272e9i	−0.0113170	+	0.223993i
$701$			1.28742e10i			1.41159i	0.708418	+	0.705794i	$0.249409\pi$
$701$			1.28742e10i			1.41159i	−0.708418	+	0.705794i	$0.750591\pi$
$702$		0			0
$703$			3.30303e9i			0.358565i
$704$	−1.02611e10	−	1.56595e9i	−1.10838	−	0.169151i
$705$		0			0
$706$	−1.29043e8	+	5.11145e9i	−0.0138012	+	0.546673i
$707$	1.18454e10			1.26061
$708$		0			0
$709$	1.58274e10			1.66782			0.833909	−	0.551901i	$-0.186097\pi$
$709$	1.58274e10			1.66782			0.833909	+	0.551901i	$0.186097\pi$
$710$	−1.68661e8	+	6.68075e9i	−0.0176852	+	0.700520i
$711$		0			0
$712$	8.43199e8	−	1.11143e10i	0.0875488	−	1.15399i
$713$			7.72582e8i			0.0798236i
$714$		0			0
$715$		−	3.25909e9i		−	0.333446i
$716$	1.09451e10	+	5.52988e8i	1.11436	+	0.0563015i
$717$		0			0
$718$	−1.90261e9	−	4.80328e7i	−0.191829	−	0.00484287i
$719$	9.93738e9			0.997059			0.498529	−	0.866873i	$-0.333874\pi$
$719$	9.93738e9			0.997059			0.498529	+	0.866873i	$0.333874\pi$
$720$		0			0
$721$	9.25366e9			0.919476
$722$	−8.44781e9	−	2.13271e8i	−0.835341	−	0.0210888i
$723$		0			0
$724$	−1.54067e10	−	7.78403e8i	−1.50877	−	0.0762289i
$725$		−	2.73611e9i		−	0.266655i
$726$		0			0
$727$			8.00923e9i			0.773073i	0.922274	+	0.386536i	$0.126329\pi$
$727$			8.00923e9i			0.773073i	−0.922274	+	0.386536i	$0.873671\pi$
$728$	5.87276e8	−	7.74094e9i	0.0564134	−	0.743590i
$729$		0			0
$730$	−1.95131e8	+	7.72926e9i	−0.0185651	+	0.735374i
$731$	3.70573e9			0.350883
$732$		0			0
$733$	−7.14827e9			−0.670405			−0.335202	−	0.942146i	$-0.608805\pi$
$733$	−7.14827e9			−0.670405			−0.335202	+	0.942146i	$0.608805\pi$
$734$	−1.08069e8	+	4.28068e9i	−0.0100871	+	0.399555i
$735$		0			0
$736$	2.00930e9	+	2.54933e8i	0.185769	+	0.0235697i
$737$			1.51085e10i			1.39022i
$738$		0			0
$739$		−	1.96524e10i		−	1.79126i	−0.444796	−	0.895632i	$-0.646724\pi$
$739$		−	1.96524e10i		−	1.79126i	0.444796	−	0.895632i	$-0.353276\pi$
$740$	2.19986e8	−	4.35411e9i	0.0199565	−	0.394992i
$741$		0			0
$742$	1.06007e10	+	2.67624e8i	0.952627	+	0.0240498i
$743$	−1.75981e10			−1.57400			−0.787001	−	0.616952i	$-0.788367\pi$
$743$	−1.75981e10			−1.57400			−0.787001	+	0.616952i	$0.788367\pi$
$744$		0			0
$745$	−5.62692e9			−0.498567
$746$	1.93458e9	+	4.88399e7i	0.170608	+	0.00430714i
$747$		0			0
$748$	6.76434e8	−	1.33885e10i	0.0590976	−	1.16970i
$749$		−	2.43049e10i		−	2.11353i
$750$		0			0
$751$			9.47530e9i			0.816306i	0.912913	+	0.408153i	$0.133827\pi$
$751$			9.47530e9i			0.816306i	−0.912913	+	0.408153i	$0.866173\pi$
$752$	−1.86766e10	−	1.89205e9i	−1.60153	−	0.162245i
$753$		0			0
$754$	−2.63386e8	+	1.04329e10i	−0.0223765	+	0.886348i
$755$	7.79614e9			0.659273
$756$		0			0
$757$	−2.01517e10			−1.68840			−0.844202	−	0.536025i	$-0.819925\pi$
$757$	−2.01517e10			−1.68840			−0.844202	+	0.536025i	$0.819925\pi$
$758$	3.98182e8	−	1.57722e10i	0.0332078	−	1.31538i
$759$		0			0
$760$	−2.18805e9	−	1.65999e8i	−0.180805	−	0.0137170i
$761$			7.69576e9i			0.633002i	0.948592	+	0.316501i	$0.102508\pi$
$761$			7.69576e9i			0.633002i	−0.948592	+	0.316501i	$0.897492\pi$
$762$		0			0
$763$			1.38242e10i			1.12669i
$764$	3.95201e9	+	1.99670e8i	0.320621	+	0.0161989i
$765$		0			0
$766$	2.35097e9	+	5.93519e7i	0.188993	+	0.00477127i
$767$	1.64621e9			0.131735
$768$		0			0
$769$	−4.27670e9			−0.339131			−0.169565	−	0.985519i	$-0.554236\pi$
$769$	−4.27670e9			−0.339131			−0.169565	+	0.985519i	$0.554236\pi$
$770$	−7.12099e9	−	1.79775e8i	−0.562112	−	0.0141909i
$771$		0			0
$772$	−2.28675e10	−	1.15535e9i	−1.78878	−	0.0903759i
$773$		−	1.72300e10i		−	1.34171i	−0.741590	−	0.670854i	$-0.765928\pi$
$773$		−	1.72300e10i		−	1.34171i	0.741590	−	0.670854i	$-0.234072\pi$
$774$		0			0
$775$			1.10478e9i			0.0852552i
$776$	−2.08096e10	−	1.57874e9i	−1.59863	−	0.121282i
$777$		0			0
$778$	4.62351e6	−	1.83140e8i	0.000352001	−	0.0139430i
$779$	−2.86309e8			−0.0216997
$780$		0			0
$781$	−2.33890e10			−1.75684
$782$	−6.60168e7	+	2.61496e9i	−0.00493663	+	0.195543i
$783$		0			0
$784$	−3.45703e9	−	3.50218e8i	−0.256210	−	0.0259557i
$785$		−	4.03968e9i		−	0.298059i
$786$		0			0
$787$		−	2.68815e10i		−	1.96581i	−0.184113	−	0.982905i	$-0.558941\pi$
$787$		−	2.68815e10i		−	1.96581i	0.184113	−	0.982905i	$-0.441059\pi$
$788$	6.39169e8	−	1.26509e10i	0.0465344	−	0.921041i
$789$		0			0
$790$	−2.92787e9	−	7.39163e7i	−0.211279	−	0.00533391i
$791$	−2.46390e10			−1.77013
$792$		0			0
$793$	−3.06245e9			−0.218079
$794$	−1.25794e10	−	3.17577e8i	−0.891843	−	0.0225152i
$795$		0			0
$796$	−8.69863e8	+	1.72169e10i	−0.0611301	+	1.20993i
$797$			1.01705e10i			0.711601i	0.934562	+	0.355800i	$0.115792\pi$
$797$			1.01705e10i			0.711601i	−0.934562	+	0.355800i	$0.884208\pi$
$798$		0			0
$799$		−	2.42441e10i		−	1.68148i
$800$	2.87328e9	+	3.64551e8i	0.198409	+	0.0251735i
$801$		0			0
$802$	4.64497e8	−	1.83990e10i	0.0317960	−	1.25946i
$803$	−2.70598e10			−1.84425
$804$		0			0
$805$	1.38995e9			0.0939103
$806$	1.06350e8	−	4.21257e9i	0.00715424	−	0.283384i
$807$		0			0
$808$	1.27516e9	−	1.68081e10i	0.0850406	−	1.12093i
$809$			2.85965e9i			0.189886i	0.995483	+	0.0949430i	$0.0302669\pi$
$809$			2.85965e9i			0.189886i	−0.995483	+	0.0949430i	$0.969733\pi$
$810$		0			0
$811$			1.65794e10i			1.09143i	0.837971	+	0.545714i	$0.183742\pi$
$811$			1.65794e10i			1.09143i	−0.837971	+	0.545714i	$0.816258\pi$
$812$	2.27809e10	+	1.15098e9i	1.49322	+	0.0754432i
$813$		0			0
$814$	1.52532e10	+	3.85080e8i	0.991235	+	0.0250245i
$815$	−1.22495e9			−0.0792626
$816$		0			0
$817$	2.12296e9			0.136196
$818$	2.15819e10	+	5.44851e8i	1.37865	+	0.0348050i
$819$		0			0
$820$	3.77417e8	+	1.90685e7i	0.0239042	+	0.00120773i
$821$		−	1.96549e10i		−	1.23956i	−0.784774	−	0.619782i	$-0.787221\pi$
$821$		−	1.96549e10i		−	1.23956i	0.784774	−	0.619782i	$-0.212779\pi$
$822$		0			0
$823$			2.62922e10i			1.64410i	0.569419	+	0.822048i	$0.307168\pi$
$823$			2.62922e10i			1.64410i	−0.569419	+	0.822048i	$0.692832\pi$
$824$	9.96162e8	−	1.31305e10i	0.0620276	−	0.817591i
$825$		0			0
$826$	9.08068e7	−	3.59691e9i	0.00560645	−	0.222075i
$827$	−7.90370e9			−0.485916			−0.242958	−	0.970037i	$-0.578118\pi$
$827$	−7.90370e9			−0.485916			−0.242958	+	0.970037i	$0.578118\pi$
$828$		0			0
$829$	−2.79874e10			−1.70617			−0.853085	−	0.521772i	$-0.825271\pi$
$829$	−2.79874e10			−1.70617			−0.853085	+	0.521772i	$0.825271\pi$
$830$	−3.04842e7	+	1.20750e9i	−0.00185055	+	0.0733015i
$831$		0			0
$832$	−1.09208e10	−	1.66663e9i	−0.657390	−	0.100325i
$833$		−	4.48757e9i		−	0.269001i
$834$		0			0
$835$		−	6.08016e9i		−	0.361420i
$836$	3.87520e8	−	7.67005e9i	0.0229389	−	0.454022i
$837$		0			0
$838$	2.03199e10	+	5.12990e8i	1.19280	+	0.0301131i
$839$	2.18716e10			1.27854			0.639269	−	0.768983i	$-0.279237\pi$
$839$	2.18716e10			1.27854			0.639269	+	0.768983i	$0.279237\pi$
$840$		0			0
$841$	−1.34140e10			−0.777628
$842$	3.03225e10	+	7.65515e8i	1.75054	+	0.0441938i
$843$		0			0
$844$	−1.48365e9	+	2.93654e10i	−0.0849441	+	1.68127i
$845$			4.37493e9i			0.249444i
$846$		0			0
$847$		−	5.09900e9i		−	0.288332i
$848$	1.52092e9	−	1.50131e10i	0.0856489	−	0.845447i
$849$		0			0
$850$	−9.44031e7	+	3.73937e9i	−0.00527254	+	0.208849i
$851$	−2.97729e9			−0.165603
$852$		0			0
$853$	1.59600e10			0.880465			0.440232	−	0.897884i	$-0.354896\pi$
$853$	1.59600e10			0.880465			0.440232	+	0.897884i	$0.354896\pi$
$854$	−1.68928e8	+	6.69134e9i	−0.00928109	+	0.367630i
$855$		0			0
$856$	−3.44875e10	−	2.61644e9i	−1.87933	−	0.142578i
$857$			4.74214e9i			0.257360i	0.991686	+	0.128680i	$0.0410741\pi$
$857$			4.74214e9i			0.257360i	−0.991686	+	0.128680i	$0.958926\pi$
$858$		0			0
$859$		−	2.57684e10i		−	1.38711i	−0.720402	−	0.693557i	$-0.756043\pi$
$859$		−	2.57684e10i		−	1.38711i	0.720402	−	0.693557i	$-0.243957\pi$
$860$	−2.79852e9	−	1.41392e8i	−0.150032	−	0.00758017i
$861$		0			0
$862$	−2.71346e10	−	6.85033e8i	−1.44294	−	0.0364281i
$863$	1.98251e9			0.104997			0.0524986	−	0.998621i	$-0.483281\pi$
$863$	1.98251e9			0.104997			0.0524986	+	0.998621i	$0.483281\pi$
$864$		0			0
$865$	4.85358e9			0.254980
$866$	1.39254e10	+	3.51558e8i	0.728612	+	0.0183944i
$867$		0			0
$868$	−9.19844e9	−	4.64739e8i	−0.477414	−	0.0241207i
$869$		−	1.02503e10i		−	0.529869i
$870$		0			0
$871$			1.60798e10i			0.824552i
$872$	1.96159e10	+	1.48818e9i	1.00184	+	0.0760062i
$873$		0			0
$874$	−3.78201e7	+	1.49808e9i	−0.00191616	+	0.0759003i
$875$	1.98761e9			0.100300
$876$		0			0
$877$	−2.89235e9			−0.144795			−0.0723973	−	0.997376i	$-0.523065\pi$
$877$	−2.89235e9			−0.144795			−0.0723973	+	0.997376i	$0.523065\pi$
$878$	−6.76110e8	+	2.67811e10i	−0.0337122	+	1.33536i
$879$		0			0
$880$	−1.02167e9	+	1.00850e10i	−0.0505384	+	0.498869i
$881$			1.17827e10i			0.580538i	0.956945	+	0.290269i	$0.0937448\pi$
$881$			1.17827e10i			0.580538i	−0.956945	+	0.290269i	$0.906255\pi$
$882$		0			0
$883$			5.83580e9i			0.285258i	0.989776	+	0.142629i	$0.0455556\pi$
$883$			5.83580e9i			0.285258i	−0.989776	+	0.142629i	$0.954444\pi$
$884$	7.19924e8	−	1.42492e10i	0.0350513	−	0.693759i
$885$		0			0
$886$	2.24874e10	+	5.67712e8i	1.08623	+	0.0274227i
$887$	8.23689e9			0.396306			0.198153	−	0.980171i	$-0.436506\pi$
$887$	8.23689e9			0.396306			0.198153	+	0.980171i	$0.436506\pi$
$888$		0			0
$889$	2.75431e10			1.31479
$890$	−1.08815e10	−	2.74712e8i	−0.517398	−	0.0130621i
$891$		0			0
$892$	−1.04892e9	+	2.07609e10i	−0.0494840	+	0.979420i
$893$		−	1.38891e10i		−	0.652670i
$894$		0			0
$895$		−	1.07022e10i		−	0.498992i
$896$	−4.24393e9	+	2.37696e10i	−0.197102	+	1.10394i
$897$		0			0
$898$	−7.37865e7	+	2.92273e9i	−0.00340024	+	0.134686i
$899$	1.23814e10			0.568344
$900$		0			0
$901$	1.94886e10			0.887654
$902$	−3.33790e7	+	1.32216e9i	−0.00151443	+	0.0599877i
$903$		0			0
$904$	−2.65240e9	+	3.49615e10i	−0.119412	+	1.57399i
$905$			1.50648e10i			0.675605i
$906$		0			0
$907$			3.33720e9i			0.148510i	0.997239	+	0.0742552i	$0.0236579\pi$
$907$			3.33720e9i			0.148510i	−0.997239	+	0.0742552i	$0.976342\pi$
$908$	3.34597e10	+	1.69051e9i	1.48327	+	0.0749405i
$909$		0			0
$910$	−7.57882e9	−	1.91333e8i	−0.333393	−	0.00841676i
$911$	−4.07441e10			−1.78546			−0.892731	−	0.450589i	$-0.851214\pi$
$911$	−4.07441e10			−1.78546			−0.892731	+	0.450589i	$0.851214\pi$
$912$		0			0
$913$	−4.22739e9			−0.183834
$914$	−1.15903e10	−	2.92606e8i	−0.502092	−	0.0126757i
$915$		0			0
$916$	−3.14168e9	−	1.58730e8i	−0.135060	−	0.00682376i
$917$			1.87015e10i			0.800912i
$918$		0			0
$919$		−	1.03514e10i		−	0.439943i	−0.975506	−	0.219972i	$-0.929404\pi$
$919$		−	1.03514e10i		−	0.439943i	0.975506	−	0.219972i	$-0.0705965\pi$
$920$	1.49629e8	−	1.97227e9i	0.00633516	−	0.0835044i
$921$		0			0
$922$	−4.74217e8	+	1.87840e10i	−0.0199260	+	0.789279i
$923$	−2.48927e10			−1.04200
$924$		0			0
$925$	−4.25748e9			−0.176871
$926$	3.81251e7	−	1.51016e9i	0.00157787	−	0.0625005i
$927$		0			0
$928$	4.08556e9	−	3.22011e10i	0.167816	−	1.32267i
$929$		−	3.99110e10i		−	1.63319i	−0.577210	−	0.816596i	$-0.695859\pi$
$929$		−	3.99110e10i		−	1.63319i	0.577210	−	0.816596i	$-0.304141\pi$
$930$		0			0
$931$		−	2.57087e9i		−	0.104413i
$932$	−2.43370e8	+	4.81695e9i	−0.00984718	+	0.194902i
$933$		0			0
$934$	3.90247e10	+	9.85207e8i	1.56720	+	0.0395652i
$935$	−1.30913e10			−0.523773
$936$		0			0
$937$	1.42043e10			0.564069			0.282034	−	0.959404i	$-0.408991\pi$
$937$	1.42043e10			0.564069			0.282034	+	0.959404i	$0.408991\pi$
$938$	3.51338e10	+	8.86979e8i	1.39000	+	0.0350916i
$939$		0			0
$940$	−9.25031e8	+	1.83088e10i	−0.0363253	+	0.718974i
$941$		−	9.73811e9i		−	0.380988i	−0.981688	−	0.190494i	$-0.938991\pi$
$941$		−	9.73811e9i		−	0.380988i	0.981688	−	0.190494i	$-0.0610089\pi$
$942$		0			0
$943$		−	2.58074e8i		−	0.0100220i
$944$	−5.09407e9	−	5.16060e8i	−0.197089	−	0.0199663i
$945$		0			0
$946$	2.47503e8	−	9.80373e9i	0.00950519	−	0.376506i
$947$	−2.30378e10			−0.881486			−0.440743	−	0.897633i	$-0.645285\pi$
$947$	−2.30378e10			−0.881486			−0.440743	+	0.897633i	$0.645285\pi$
$948$		0			0
$949$	−2.87995e10			−1.09384
$950$	−5.40822e7	+	2.14223e9i	−0.00204655	+	0.0810650i
$951$		0			0
$952$	−3.10943e10	−	2.35901e9i	−1.16802	−	0.0886135i
$953$		−	3.13419e10i		−	1.17300i	−0.809948	−	0.586502i	$-0.800505\pi$
$953$		−	3.13419e10i		−	1.17300i	0.809948	−	0.586502i	$-0.199495\pi$
$954$		0			0
$955$		−	3.86431e9i		−	0.143569i
$956$	2.03162e10	+	1.02645e9i	0.752040	+	0.0379958i
$957$		0			0
$958$	−1.34132e10	−	3.38628e8i	−0.492895	−	0.0124435i
$959$	3.26931e10			1.19699
$960$		0			0
$961$	2.25133e10			0.818289
$962$	1.62339e10	+	4.09838e8i	0.587910	+	0.0148422i
$963$		0			0
$964$	4.41341e10	+	2.22982e9i	1.58674	+	0.0801679i
$965$			2.23600e10i			0.800988i
$966$		0			0
$967$			9.68193e9i			0.344325i	0.985069	+	0.172163i	$0.0550755\pi$
$967$			9.68193e9i			0.344325i	−0.985069	+	0.172163i	$0.944925\pi$
$968$	−7.23524e9	−	5.48911e8i	−0.256383	−	0.0194508i
$969$		0			0
$970$	−5.14351e8	+	2.03738e10i	−0.0180950	+	0.716754i
$971$	−2.27423e10			−0.797200			−0.398600	−	0.917125i	$-0.630504\pi$
$971$	−2.27423e10			−0.797200			−0.398600	+	0.917125i	$0.630504\pi$
$972$		0			0
$973$	−1.33615e10			−0.465008
$974$	1.22017e9	−	4.83317e10i	0.0423120	−	1.67601i
$975$		0			0
$976$	9.47651e9	+	9.60028e8i	0.326268	+	0.0330529i
$977$			5.49219e10i			1.88414i	0.335410	+	0.942072i	$0.391125\pi$
$977$			5.49219e10i			1.88414i	−0.335410	+	0.942072i	$0.608875\pi$
$978$		0			0
$979$		−	3.80957e10i		−	1.29759i
$980$	−1.71223e8	+	3.38896e9i	−0.00581126	+	0.115020i
$981$		0			0
$982$	2.69352e9	+	6.80001e7i	0.0907676	+	0.00229150i
$983$	−2.85112e9			−0.0957365			−0.0478683	−	0.998854i	$-0.515243\pi$
$983$	−2.85112e9			−0.0957365			−0.0478683	+	0.998854i	$0.515243\pi$
$984$		0			0
$985$	−1.23701e10			−0.412427
$986$	4.19075e10	+	1.05799e9i	1.39227	+	0.0351488i
$987$		0			0
$988$	4.12434e8	−	8.16319e9i	0.0136052	−	0.269284i
$989$			1.91359e9i			0.0629018i
$990$		0			0
$991$		−	4.09672e10i		−	1.33714i	−0.743647	−	0.668572i	$-0.766906\pi$
$991$		−	4.09672e10i		−	1.33714i	0.743647	−	0.668572i	$-0.233094\pi$
$992$	−1.64966e9	+	1.30021e10i	−0.0536542	+	0.422886i
$993$		0			0
$994$	−1.37311e9	+	5.43896e10i	−0.0443457	+	1.75656i
$995$	1.68349e10			0.541787
$996$		0			0
$997$	−4.90949e10			−1.56893			−0.784465	−	0.620173i	$-0.787062\pi$
$997$	−4.90949e10			−1.56893			−0.784465	+	0.620173i	$0.787062\pi$
$998$	−1.15091e9	+	4.55882e10i	−0.0366508	+	1.45176i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.8.e.a.71.1	✓	56
3.2	odd	2	inner	180.8.e.a.71.56	yes	56
4.3	odd	2	inner	180.8.e.a.71.55	yes	56
12.11	even	2	inner	180.8.e.a.71.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.8.e.a.71.1	✓	56	1.1	even	1	trivial
180.8.e.a.71.2	yes	56	12.11	even	2	inner
180.8.e.a.71.55	yes	56	4.3	odd	2	inner
180.8.e.a.71.56	yes	56	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	180.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.3101 - 0.285532i) q^{2} +(127.837 + 6.45880i) q^{4} -125.000i q^{5} -1017.66i q^{7} +(-1444.01 - 109.551i) q^{8} +O(q^{10})\)	\(q+(-11.3101 - 0.285532i) q^{2} +(127.837 + 6.45880i) q^{4} -125.000i q^{5} -1017.66i q^{7} +(-1444.01 - 109.551i) q^{8} +(-35.6915 + 1413.76i) q^{10} -4949.52 q^{11} -5267.74 q^{13} +(-290.573 + 11509.8i) q^{14} +(16300.6 + 1651.35i) q^{16} +21159.8i q^{17} +12122.1i q^{19} +(807.350 - 15979.6i) q^{20} +(55979.5 + 1413.25i) q^{22} -10926.7 q^{23} -15625.0 q^{25} +(59578.6 + 1504.11i) q^{26} +(6572.83 - 130094. i) q^{28} +175111. i q^{29} -70706.1i q^{31} +(-183890. - 23331.2i) q^{32} +(6041.80 - 239319. i) q^{34} -127207. q^{35} +272479. q^{37} +(3461.26 - 137103. i) q^{38} +(-13693.9 + 180501. i) q^{40} +23618.7i q^{41} -175131. i q^{43} +(-632731. - 31967.9i) q^{44} +(123582. + 3119.92i) q^{46} -1.14576e6 q^{47} -212080. q^{49} +(176720. + 4461.44i) q^{50} +(-673411. - 34023.2i) q^{52} -921020. i q^{53} +618689. i q^{55} +(-111485. + 1.46950e6i) q^{56} +(49999.8 - 1.98052e6i) q^{58} -312509. q^{59} +581361. q^{61} +(-20188.9 + 799693. i) q^{62} +(2.07315e6 + 316385. i) q^{64} +658467. i q^{65} -3.05251e6i q^{67} +(-136667. + 2.70500e6i) q^{68} +(1.43872e6 + 36321.7i) q^{70} +4.72551e6 q^{71} +5.46716e6 q^{73} +(-3.08176e6 - 77801.5i) q^{74} +(-78294.5 + 1.54966e6i) q^{76} +5.03690e6i q^{77} +2.07098e6i q^{79} +(206418. - 2.03757e6i) q^{80} +(6743.89 - 267130. i) q^{82} +854102. q^{83} +2.64497e6 q^{85} +(-50005.4 + 1.98075e6i) q^{86} +(7.14713e6 + 542226. i) q^{88} +7.69685e6i q^{89} +5.36074e6i q^{91} +(-1.39683e6 - 70573.2i) q^{92} +(1.29587e7 + 327152. i) q^{94} +1.51527e6 q^{95} +1.44110e7 q^{97} +(2.39865e6 + 60555.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 52 q^{4}+O(q^{10}) \) 56 * q + 52 * q^4	\( 56 q + 52 q^{4} - 6500 q^{10} + 14128 q^{13} - 8060 q^{16} + 259088 q^{22} - 875000 q^{25} - 490976 q^{28} + 40912 q^{34} + 1268048 q^{37} - 266500 q^{40} + 3108200 q^{46} - 3522056 q^{49} - 8882216 q^{52} + 8807592 q^{58} - 3944912 q^{61} - 16633580 q^{64} + 4533000 q^{70} + 7602384 q^{73} - 38876976 q^{76} + 33213064 q^{82} - 15068000 q^{85} - 56145472 q^{88} + 29409456 q^{94} - 45595824 q^{97}+O(q^{100}) \) 56 * q + 52 * q^4 - 6500 * q^10 + 14128 * q^13 - 8060 * q^16 + 259088 * q^22 - 875000 * q^25 - 490976 * q^28 + 40912 * q^34 + 1268048 * q^37 - 266500 * q^40 + 3108200 * q^46 - 3522056 * q^49 - 8882216 * q^52 + 8807592 * q^58 - 3944912 * q^61 - 16633580 * q^64 + 4533000 * q^70 + 7602384 * q^73 - 38876976 * q^76 + 33213064 * q^82 - 15068000 * q^85 - 56145472 * q^88 + 29409456 * q^94 - 45595824 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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