LMFDB - Embedded newform 84.12.i.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,12,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, 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:	$64.5408271670$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 $ x^16 - 581500324x^14 - 481772282104x^13 + 132272376701859942x^12 + 189765040124256066208x^11 - 14668309022748191106194508x^10 - 25034330150368988089577197656x^9 + 804524023197576594568815873370179x^8 + 1124828921377792402289540847268007968x^7 - 19980431516277460534216470290766973558668x^6 + 592727132887361668148704829618109324342008x^5 + 215459975341822734071937522290785139860745873306x^4 - 372150170517680072482976606267991582419751904690704x^3 - 31534379943215460069637664338468383174583531082850128x^2 + 257934680050232001165280545701170549413209663811915341424x + 79978257504936591964642108900330900905737463001503418421877
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{15}\cdot 7^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$10810.2 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.12.i.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-121.500 - 210.444i) q^{3} +(-5539.86 + 9595.32i) q^{5} +(-32020.8 - 30854.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})$	\(q+(-121.500 - 210.444i) q^{3} +(-5539.86 + 9595.32i) q^{5} +(-32020.8 - 30854.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(451860. + 782645. i) q^{11} -761355. q^{13} +2.69237e6 q^{15} +(2.39149e6 + 4.14219e6i) q^{17} +(-2.25438e6 + 3.90470e6i) q^{19} +(-2.60260e6 + 1.04874e7i) q^{21} +(-2.38885e7 + 4.13761e7i) q^{23} +(-3.69661e7 - 6.40271e7i) q^{25} +1.43489e7 q^{27} +1.65205e8 q^{29} +(-2.95464e7 - 5.11759e7i) q^{31} +(1.09802e8 - 1.90183e8i) q^{33} +(4.73449e8 - 1.36321e8i) q^{35} +(1.08530e8 - 1.87980e8i) q^{37} +(9.25047e7 + 1.60223e8i) q^{39} -5.52269e8 q^{41} -1.04028e9 q^{43} +(-3.27123e8 - 5.66594e8i) q^{45} +(-6.93035e7 + 1.20037e8i) q^{47} +(7.33368e7 + 1.97597e9i) q^{49} +(5.81133e8 - 1.00655e9i) q^{51} +(2.34318e9 + 4.05851e9i) q^{53} -1.00130e10 q^{55} +1.09563e9 q^{57} +(-4.49535e9 - 7.78617e9i) q^{59} +(-1.08443e8 + 1.87828e8i) q^{61} +(2.52323e9 - 7.26517e8i) q^{63} +(4.21780e9 - 7.30545e9i) q^{65} +(-8.64085e9 - 1.49664e10i) q^{67} +1.16098e10 q^{69} -5.28267e9 q^{71} +(-5.55061e9 - 9.61394e9i) q^{73} +(-8.98276e9 + 1.55586e10i) q^{75} +(9.67912e9 - 3.90028e10i) q^{77} +(2.14340e9 - 3.71248e9i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -4.61200e10 q^{83} -5.29942e10 q^{85} +(-2.00724e10 - 3.47665e10i) q^{87} +(-8.53894e9 + 1.47899e10i) q^{89} +(2.43792e10 + 2.34912e10i) q^{91} +(-7.17979e9 + 1.24358e10i) q^{93} +(-2.49779e10 - 4.32631e10i) q^{95} +1.57413e11 q^{97} -5.33638e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) $ 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9	$ 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) $ 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9 - 222796 * q^11 + 2703176 * q^13 + 1047816 * q^15 + 5114600 * q^17 + 6910556 * q^19 - 18340668 * q^21 - 51387712 * q^23 - 191456372 * q^25 + 229582512 * q^27 + 118854616 * q^29 + 164659160 * q^31 - 54139428 * q^33 + 55239344 * q^35 + 75658364 * q^37 - 328435884 * q^39 - 1815568608 * q^41 + 10754408 * q^43 - 127309644 * q^45 - 1034359464 * q^47 + 4123496848 * q^49 + 1242847800 * q^51 - 665159988 * q^53 - 1264543896 * q^55 - 3358530216 * q^57 + 1040514580 * q^59 - 14391208024 * q^61 + 1474099236 * q^63 - 20938150200 * q^65 - 33307097284 * q^67 + 24974428032 * q^69 + 65848902896 * q^71 + 17709749204 * q^73 - 46523898396 * q^75 + 8594484604 * q^77 - 26626784032 * q^79 - 27894275208 * q^81 - 210306955048 * q^83 - 25867402032 * q^85 - 14440835844 * q^87 - 55951560072 * q^89 + 66078280292 * q^91 + 40012175880 * q^93 + 106810047392 * q^95 - 156216030712 * q^97 + 26311762008 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−121.500	−	210.444i	−0.288675	−	0.500000i
$3$	−121.500	−	210.444i	−0.288675	−	0.500000i
$4$		0			0
$5$	−5539.86	+	9595.32i	−0.792801	+	1.37317i	0.131426	+	0.991326i	$0.458044\pi$
$5$	−5539.86	+	9595.32i	−0.792801	+	1.37317i	−0.924226	+	0.381845i	$0.875289\pi$
$6$		0			0
$7$	−32020.8	−	30854.4i	−0.720100	−	0.693870i
$7$	−32020.8	−	30854.4i	−0.720100	−	0.693870i
$8$		0			0
$9$	−29524.5	+	51137.9i	−0.166667	+	0.288675i
$10$		0			0
$11$	451860.	+	782645.i	0.845949	+	1.46523i	0.884794	+	0.465982i	$0.154299\pi$
$11$	451860.	+	782645.i	0.845949	+	1.46523i	−0.0388451	+	0.999245i	$0.512368\pi$
$12$		0			0
$13$	−761355.			−0.568721			−0.284360	−	0.958717i	$-0.591781\pi$
$13$	−761355.			−0.568721			−0.284360	+	0.958717i	$0.591781\pi$
$14$		0			0
$15$	2.69237e6			0.915447
$16$		0			0
$17$	2.39149e6	+	4.14219e6i	0.408508	+	0.707556i	0.994723	−	0.102599i	$-0.0327160\pi$
$17$	2.39149e6	+	4.14219e6i	0.408508	+	0.707556i	−0.586215	+	0.810155i	$0.699383\pi$
$18$		0			0
$19$	−2.25438e6	+	3.90470e6i	−0.208873	+	0.361779i	−0.951360	−	0.308082i	$-0.900313\pi$
$19$	−2.25438e6	+	3.90470e6i	−0.208873	+	0.361779i	0.742487	+	0.669861i	$0.233646\pi$
$20$		0			0
$21$	−2.60260e6	+	1.04874e7i	−0.139060	+	0.560353i
$22$		0			0
$23$	−2.38885e7	+	4.13761e7i	−0.773901	+	1.34044i	0.161509	+	0.986871i	$0.448364\pi$
$23$	−2.38885e7	+	4.13761e7i	−0.773901	+	1.34044i	−0.935410	+	0.353565i	$0.884969\pi$
$24$		0			0
$25$	−3.69661e7	−	6.40271e7i	−0.757065	−	1.31128i
$26$		0			0
$27$	1.43489e7			0.192450
$28$		0			0
$29$	1.65205e8			1.49567			0.747833	−	0.663887i	$-0.231095\pi$
$29$	1.65205e8			1.49567			0.747833	+	0.663887i	$0.231095\pi$
$30$		0			0
$31$	−2.95464e7	−	5.11759e7i	−0.185360	−	0.321053i	0.758338	−	0.651862i	$-0.226012\pi$
$31$	−2.95464e7	−	5.11759e7i	−0.185360	−	0.321053i	−0.943698	+	0.330809i	$0.892678\pi$
$32$		0			0
$33$	1.09802e8	−	1.90183e8i	0.488409	−	0.845949i
$34$		0			0
$35$	4.73449e8	−	1.36321e8i	1.52370	−	0.438720i
$36$		0			0
$37$	1.08530e8	−	1.87980e8i	0.257301	−	0.445658i	−0.708217	−	0.705995i	$-0.750500\pi$
$37$	1.08530e8	−	1.87980e8i	0.257301	−	0.445658i	0.965518	+	0.260337i	$0.0838335\pi$
$38$		0			0
$39$	9.25047e7	+	1.60223e8i	0.164176	+	0.284360i
$40$		0			0
$41$	−5.52269e8			−0.744456			−0.372228	−	0.928141i	$-0.621406\pi$
$41$	−5.52269e8			−0.744456			−0.372228	+	0.928141i	$0.621406\pi$
$42$		0			0
$43$	−1.04028e9			−1.07913			−0.539563	−	0.841945i	$-0.681411\pi$
$43$	−1.04028e9			−1.07913			−0.539563	+	0.841945i	$0.681411\pi$
$44$		0			0
$45$	−3.27123e8	−	5.66594e8i	−0.264267	−	0.457724i
$46$		0			0
$47$	−6.93035e7	+	1.20037e8i	−0.0440775	+	0.0763445i	−0.887222	−	0.461342i	$-0.847368\pi$
$47$	−6.93035e7	+	1.20037e8i	−0.0440775	+	0.0763445i	0.843145	+	0.537686i	$0.180702\pi$
$48$		0			0
$49$	7.33368e7	+	1.97597e9i	0.0370889	+	0.999312i
$50$		0			0
$51$	5.81133e8	−	1.00655e9i	0.235852	−	0.408508i
$52$		0			0
$53$	2.34318e9	+	4.05851e9i	0.769641	+	1.33306i	0.937758	+	0.347290i	$0.112898\pi$
$53$	2.34318e9	+	4.05851e9i	0.769641	+	1.33306i	−0.168117	+	0.985767i	$0.553768\pi$
$54$		0			0
$55$	−1.00130e10			−2.68268
$56$		0			0
$57$	1.09563e9			0.241186
$58$		0			0
$59$	−4.49535e9	−	7.78617e9i	−0.818610	−	1.41787i	−0.906706	−	0.421763i	$-0.861412\pi$
$59$	−4.49535e9	−	7.78617e9i	−0.818610	−	1.41787i	0.0880959	−	0.996112i	$-0.471922\pi$
$60$		0			0
$61$	−1.08443e8	+	1.87828e8i	−0.0164394	+	0.0284739i	−0.874128	−	0.485695i	$-0.838566\pi$
$61$	−1.08443e8	+	1.87828e8i	−0.0164394	+	0.0284739i	0.857689	+	0.514169i	$0.171900\pi$
$62$		0			0
$63$	2.52323e9	−	7.26517e8i	0.320320	−	0.0922301i
$64$		0			0
$65$	4.21780e9	−	7.30545e9i	0.450882	−	0.780951i
$66$		0			0
$67$	−8.64085e9	−	1.49664e10i	−0.781889	−	1.35427i	−0.930840	−	0.365426i	$-0.880923\pi$
$67$	−8.64085e9	−	1.49664e10i	−0.781889	−	1.35427i	0.148952	−	0.988844i	$-0.452410\pi$
$68$		0			0
$69$	1.16098e10			0.893624
$70$		0			0
$71$	−5.28267e9			−0.347482			−0.173741	−	0.984791i	$-0.555586\pi$
$71$	−5.28267e9			−0.347482			−0.173741	+	0.984791i	$0.555586\pi$
$72$		0			0
$73$	−5.55061e9	−	9.61394e9i	−0.313375	−	0.542782i	0.665715	−	0.746206i	$-0.268127\pi$
$73$	−5.55061e9	−	9.61394e9i	−0.313375	−	0.542782i	−0.979091	+	0.203424i	$0.934793\pi$
$74$		0			0
$75$	−8.98276e9	+	1.55586e10i	−0.437092	+	0.757065i
$76$		0			0
$77$	9.67912e9	−	3.90028e10i	0.407509	−	1.64209i
$78$		0			0
$79$	2.14340e9	−	3.71248e9i	0.0783709	−	0.135742i	−0.824176	−	0.566333i	$-0.808361\pi$
$79$	2.14340e9	−	3.71248e9i	0.0783709	−	0.135742i	0.902547	+	0.430591i	$0.141695\pi$
$80$		0			0
$81$	−1.74339e9	−	3.01964e9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−4.61200e10			−1.28517			−0.642584	−	0.766216i	$-0.722137\pi$
$83$	−4.61200e10			−1.28517			−0.642584	+	0.766216i	$0.722137\pi$
$84$		0			0
$85$	−5.29942e10			−1.29546
$86$		0			0
$87$	−2.00724e10	−	3.47665e10i	−0.431761	−	0.747833i
$88$		0			0
$89$	−8.53894e9	+	1.47899e10i	−0.162091	+	0.280750i	−0.935618	−	0.353013i	$-0.885157\pi$
$89$	−8.53894e9	+	1.47899e10i	−0.162091	+	0.280750i	0.773527	+	0.633763i	$0.218490\pi$
$90$		0			0
$91$	2.43792e10	+	2.34912e10i	0.409536	+	0.394618i
$92$		0			0
$93$	−7.17979e9	+	1.24358e10i	−0.107018	+	0.185360i
$94$		0			0
$95$	−2.49779e10	−	4.32631e10i	−0.331190	−	0.573637i
$96$		0			0
$97$	1.57413e11			1.86121			0.930605	−	0.366026i	$-0.119282\pi$
$97$	1.57413e11			1.86121			0.930605	+	0.366026i	$0.119282\pi$
$98$		0			0
$99$	−5.33638e10			−0.563966
$100$		0			0
$101$	−7.77841e10	−	1.34726e11i	−0.736416	−	1.27551i	−0.954099	−	0.299490i	$-0.903183\pi$
$101$	−7.77841e10	−	1.34726e11i	−0.736416	−	1.27551i	0.217683	−	0.976019i	$-0.430150\pi$
$102$		0			0
$103$	6.88269e10	−	1.19212e11i	0.584997	−	1.01324i	−0.409879	−	0.912140i	$-0.634429\pi$
$103$	6.88269e10	−	1.19212e11i	0.584997	−	1.01324i	0.994876	−	0.101105i	$-0.0322377\pi$
$104$		0			0
$105$	−8.62119e10	−	8.30716e10i	−0.659214	−	0.635201i
$106$		0			0
$107$	−9.51994e10	+	1.64890e11i	−0.656181	+	1.13654i	0.325416	+	0.945571i	$0.394496\pi$
$107$	−9.51994e10	+	1.64890e11i	−0.656181	+	1.13654i	−0.981596	+	0.190967i	$0.938838\pi$
$108$		0			0
$109$	−9.45648e10	−	1.63791e11i	−0.588686	−	1.01963i	−0.994405	−	0.105636i	$-0.966312\pi$
$109$	−9.45648e10	−	1.63791e11i	−0.588686	−	1.01963i	0.405719	−	0.913998i	$-0.367021\pi$
$110$		0			0
$111$	−5.27457e10			−0.297106
$112$		0			0
$113$	−1.29301e11			−0.660190			−0.330095	−	0.943948i	$-0.607081\pi$
$113$	−1.29301e11			−0.660190			−0.330095	+	0.943948i	$0.607081\pi$
$114$		0			0
$115$	−2.64678e11	−	4.58436e11i	−1.22710	−	2.12540i
$116$		0			0
$117$	2.24786e10	−	3.89341e10i	0.0947868	−	0.164176i
$118$		0			0
$119$	5.12273e10	−	2.06424e11i	0.196785	−	0.792962i
$120$		0			0
$121$	−2.65699e11	+	4.60205e11i	−0.931260	+	1.61299i
$122$		0			0
$123$	6.71007e10	+	1.16222e11i	0.214906	+	0.372228i
$124$		0			0
$125$	2.78146e11			0.815206
$126$		0			0
$127$	1.94863e10			0.0523369			0.0261685	−	0.999658i	$-0.491669\pi$
$127$	1.94863e10			0.0523369			0.0261685	+	0.999658i	$0.491669\pi$
$128$		0			0
$129$	1.26394e11	+	2.18920e11i	0.311517	+	0.539563i
$130$		0			0
$131$	−1.37802e10	+	2.38680e10i	−0.0312078	+	0.0540535i	−0.881207	−	0.472730i	$-0.843269\pi$
$131$	−1.37802e10	+	2.38680e10i	−0.0312078	+	0.0540535i	0.850000	+	0.526783i	$0.176602\pi$
$132$		0			0
$133$	1.92665e11	−	5.54741e10i	0.401437	−	0.115586i
$134$		0			0
$135$	−7.94910e10	+	1.37682e11i	−0.152575	+	0.264267i
$136$		0			0
$137$	1.55036e11	+	2.68531e11i	0.274454	+	0.475369i	0.969997	−	0.243116i	$-0.0781694\pi$
$137$	1.55036e11	+	2.68531e11i	0.274454	+	0.475369i	−0.695543	+	0.718485i	$0.744836\pi$
$138$		0			0
$139$	5.28928e11			0.864600			0.432300	−	0.901730i	$-0.357702\pi$
$139$	5.28928e11			0.864600			0.432300	+	0.901730i	$0.357702\pi$
$140$		0			0
$141$	3.36815e10			0.0508963
$142$		0			0
$143$	−3.44026e11	−	5.95871e11i	−0.481109	−	0.833305i
$144$		0			0
$145$	−9.15213e11	+	1.58520e12i	−1.18576	+	2.05380i
$146$		0			0
$147$	4.06920e11	−	2.55513e11i	0.488949	−	0.307021i
$148$		0			0
$149$	2.21201e11	−	3.83131e11i	0.246753	−	0.427389i	−0.715870	−	0.698234i	$-0.753970\pi$
$149$	2.21201e11	−	3.83131e11i	0.246753	−	0.427389i	0.962623	+	0.270845i	$0.0873030\pi$
$150$		0			0
$151$	8.75046e11	+	1.51562e12i	0.907105	+	1.57115i	0.818066	+	0.575124i	$0.195046\pi$
$151$	8.75046e11	+	1.51562e12i	0.907105	+	1.57115i	0.0890393	+	0.996028i	$0.471620\pi$
$152$		0			0
$153$	−2.82431e11			−0.272338
$154$		0			0
$155$	6.54733e11			0.587814
$156$		0			0
$157$	−6.97856e11	−	1.20872e12i	−0.583872	−	1.01130i	−0.995015	−	0.0997250i	$-0.968204\pi$
$157$	−6.97856e11	−	1.20872e12i	−0.583872	−	1.01130i	0.411143	−	0.911571i	$-0.365130\pi$
$158$		0			0
$159$	5.69393e11	−	9.86217e11i	0.444353	−	0.769641i
$160$		0			0
$161$	2.04156e12	−	5.87830e11i	1.48738	−	0.428262i
$162$		0			0
$163$	6.83315e11	−	1.18354e12i	0.465146	−	0.805656i	−0.534062	−	0.845445i	$-0.679335\pi$
$163$	6.83315e11	−	1.18354e12i	0.465146	−	0.805656i	0.999208	+	0.0397888i	$0.0126685\pi$
$164$		0			0
$165$	1.21658e12	+	2.10717e12i	0.774422	+	1.34134i
$166$		0			0
$167$	6.20052e11			0.369392			0.184696	−	0.982796i	$-0.440870\pi$
$167$	6.20052e11			0.369392			0.184696	+	0.982796i	$0.440870\pi$
$168$		0			0
$169$	−1.21250e12			−0.676557
$170$		0			0
$171$	−1.33119e11	−	2.30569e11i	−0.0696244	−	0.120593i
$172$		0			0
$173$	−3.99102e11	+	6.91264e11i	−0.195808	+	0.339149i	−0.947165	−	0.320747i	$-0.896066\pi$
$173$	−3.99102e11	+	6.91264e11i	−0.195808	+	0.339149i	0.751357	+	0.659896i	$0.229400\pi$
$174$		0			0
$175$	−7.91836e11	+	3.19077e12i	−0.364692	+	1.46955i
$176$		0			0
$177$	−1.09237e12	+	1.89204e12i	−0.472625	+	0.818610i
$178$		0			0
$179$	3.98673e11	+	6.90522e11i	0.162153	+	0.280857i	0.935641	−	0.352954i	$-0.114823\pi$
$179$	3.98673e11	+	6.90522e11i	0.162153	+	0.280857i	−0.773488	+	0.633811i	$0.781490\pi$
$180$		0			0
$181$	3.89173e12			1.48906			0.744528	−	0.667591i	$-0.232675\pi$
$181$	3.89173e12			1.48906			0.744528	+	0.667591i	$0.232675\pi$
$182$		0			0
$183$	5.27032e10			0.0189826
$184$		0			0
$185$	1.20249e12	+	2.08277e12i	0.407977	+	0.706636i
$186$		0			0
$187$	−2.16124e12	+	3.74338e12i	−0.691153	+	1.19711i
$188$		0			0
$189$	−4.59464e11	−	4.42727e11i	−0.138583	−	0.133535i
$190$		0			0
$191$	−1.64431e12	+	2.84803e12i	−0.468059	+	0.810701i	−0.999334	−	0.0364981i	$-0.988380\pi$
$191$	−1.64431e12	+	2.84803e12i	−0.468059	+	0.810701i	0.531275	+	0.847199i	$0.321713\pi$
$192$		0			0
$193$	−1.74782e12	−	3.02731e12i	−0.469819	−	0.813750i	0.529586	−	0.848257i	$-0.322347\pi$
$193$	−1.74782e12	−	3.02731e12i	−0.469819	−	0.813750i	−0.999404	+	0.0345062i	$0.989014\pi$
$194$		0			0
$195$	−2.04985e12			−0.520634
$196$		0			0
$197$	5.58940e12			1.34215			0.671074	−	0.741390i	$-0.265833\pi$
$197$	5.58940e12			1.34215			0.671074	+	0.741390i	$0.265833\pi$
$198$		0			0
$199$	2.69940e12	+	4.67549e12i	0.613162	+	1.06203i	0.990704	+	0.136035i	$0.0434359\pi$
$199$	2.69940e12	+	4.67549e12i	0.613162	+	1.06203i	−0.377542	+	0.925992i	$0.623231\pi$
$200$		0			0
$201$	−2.09973e12	+	3.63683e12i	−0.451424	+	0.781889i
$202$		0			0
$203$	−5.29000e12	−	5.09731e12i	−1.07703	−	1.03780i
$204$		0			0
$205$	3.05949e12	−	5.29920e12i	0.590205	−	1.02227i
$206$		0			0
$207$	−1.41059e12	−	2.44322e12i	−0.257967	−	0.446812i
$208$		0			0
$209$	−4.07466e12			−0.706785
$210$		0			0
$211$	8.02377e12			1.32076			0.660381	−	0.750930i	$-0.270395\pi$
$211$	8.02377e12			1.32076			0.660381	+	0.750930i	$0.270395\pi$
$212$		0			0
$213$	6.41845e11	+	1.11171e12i	0.100310	+	0.173741i
$214$		0			0
$215$	5.76299e12	−	9.98179e12i	0.855532	−	1.48182i
$216$		0			0
$217$	−6.32903e11	+	2.55033e12i	−0.0892912	+	0.359806i
$218$		0			0
$219$	−1.34880e12	+	2.33619e12i	−0.180927	+	0.313375i
$220$		0			0
$221$	−1.82078e12	−	3.15368e12i	−0.232327	−	0.402402i
$222$		0			0
$223$	2.85492e10			0.00346671			0.00173336	−	0.999998i	$-0.499448\pi$
$223$	2.85492e10			0.00346671			0.00173336	+	0.999998i	$0.499448\pi$
$224$		0			0
$225$	4.36562e12			0.504710
$226$		0			0
$227$	−6.93582e12	−	1.20132e13i	−0.763757	−	1.32287i	−0.940901	−	0.338682i	$-0.890019\pi$
$227$	−6.93582e12	−	1.20132e13i	−0.763757	−	1.32287i	0.177144	−	0.984185i	$-0.443314\pi$
$228$		0			0
$229$	−2.91500e12	+	5.04892e12i	−0.305874	+	0.529790i	−0.977456	−	0.211141i	$-0.932282\pi$
$229$	−2.91500e12	+	5.04892e12i	−0.305874	+	0.529790i	0.671581	+	0.740931i	$0.265615\pi$
$230$		0			0
$231$	−9.38392e12	+	2.70192e12i	−0.938682	+	0.270276i
$232$		0			0
$233$	7.68712e12	−	1.33145e13i	0.733341	−	1.27018i	−0.222107	−	0.975022i	$-0.571293\pi$
$233$	7.68712e12	−	1.33145e13i	0.733341	−	1.27018i	0.955447	−	0.295161i	$-0.0953734\pi$
$234$		0			0
$235$	−7.67864e11	−	1.32998e12i	−0.0698893	−	0.121052i
$236$		0			0
$237$	−1.04169e12			−0.0904950
$238$		0			0
$239$	1.72983e13			1.43488			0.717438	−	0.696622i	$-0.245314\pi$
$239$	1.72983e13			1.43488			0.717438	+	0.696622i	$0.245314\pi$
$240$		0			0
$241$	1.79662e12	+	3.11184e12i	0.142352	+	0.246560i	0.928382	−	0.371628i	$-0.121200\pi$
$241$	1.79662e12	+	3.11184e12i	0.142352	+	0.246560i	−0.786030	+	0.618188i	$0.787867\pi$
$242$		0			0
$243$	−4.23644e11	+	7.33773e11i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.93663e13	−	1.02429e13i	−1.40163	−	0.741326i
$246$		0			0
$247$	1.71639e12	−	2.97287e12i	0.118791	−	0.205751i
$248$		0			0
$249$	5.60358e12	+	9.70568e12i	0.370996	+	0.642584i
$250$		0			0
$251$	−2.07857e12			−0.131692			−0.0658461	−	0.997830i	$-0.520975\pi$
$251$	−2.07857e12			−0.131692			−0.0658461	+	0.997830i	$0.520975\pi$
$252$		0			0
$253$	−4.31770e13			−2.61872
$254$		0			0
$255$	6.43879e12	+	1.11523e13i	0.373967	+	0.647730i
$256$		0			0
$257$	4.77704e12	−	8.27408e12i	0.265783	−	0.460350i	−0.701986	−	0.712191i	$-0.747703\pi$
$257$	4.77704e12	−	8.27408e12i	0.265783	−	0.460350i	0.967768	+	0.251842i	$0.0810362\pi$
$258$		0			0
$259$	−9.27524e12	+	2.67063e12i	−0.494511	+	0.142385i
$260$		0			0
$261$	−4.87760e12	+	8.44825e12i	−0.249278	+	0.431761i
$262$		0			0
$263$	−1.62484e13	−	2.81431e13i	−0.796259	−	1.37916i	−0.922036	−	0.387103i	$-0.873476\pi$
$263$	−1.62484e13	−	2.81431e13i	−0.796259	−	1.37916i	0.125777	−	0.992059i	$-0.459858\pi$
$264$		0			0
$265$	−5.19236e13			−2.44069
$266$		0			0
$267$	4.14992e12			0.187167
$268$		0			0
$269$	5.57863e12	+	9.66247e12i	0.241485	+	0.418264i	0.961137	−	0.276070i	$-0.0890322\pi$
$269$	5.57863e12	+	9.66247e12i	0.241485	+	0.418264i	−0.719653	+	0.694334i	$0.755699\pi$
$270$		0			0
$271$	−6.81340e12	+	1.18012e13i	−0.283161	+	0.490449i	−0.972161	−	0.234312i	$-0.924716\pi$
$271$	−6.81340e12	+	1.18012e13i	−0.283161	+	0.490449i	0.689001	+	0.724761i	$0.258050\pi$
$272$		0			0
$273$	1.98151e12	−	7.98464e12i	0.0790863	−	0.318684i
$274$		0			0
$275$	3.34070e13	−	5.78626e13i	1.28088	−	2.21855i
$276$		0			0
$277$	1.14769e13	+	1.98786e13i	0.422850	+	0.732397i	0.996217	−	0.0869014i	$-0.0276965\pi$
$277$	1.14769e13	+	1.98786e13i	0.422850	+	0.732397i	−0.573367	+	0.819298i	$0.694363\pi$
$278$		0			0
$279$	3.48938e12			0.123573
$280$		0			0
$281$	−1.32538e13			−0.451291			−0.225645	−	0.974210i	$-0.572449\pi$
$281$	−1.32538e13			−0.451291			−0.225645	+	0.974210i	$0.572449\pi$
$282$		0			0
$283$	−2.36242e13	−	4.09183e13i	−0.773627	−	1.33996i	−0.935563	−	0.353161i	$-0.885107\pi$
$283$	−2.36242e13	−	4.09183e13i	−0.773627	−	1.33996i	0.161935	−	0.986801i	$-0.448226\pi$
$284$		0			0
$285$	−6.06964e12	+	1.05129e13i	−0.191212	+	0.331190i
$286$		0			0
$287$	1.76841e13	+	1.70399e13i	0.536083	+	0.516556i
$288$		0			0
$289$	5.69746e12	−	9.86829e12i	0.166243	−	0.287941i
$290$		0			0
$291$	−1.91256e13	−	3.31266e13i	−0.537285	−	0.930605i
$292$		0			0
$293$	4.50335e13			1.21833			0.609164	−	0.793045i	$-0.291505\pi$
$293$	4.50335e13			1.21833			0.609164	+	0.793045i	$0.291505\pi$
$294$		0			0
$295$	9.96144e13			2.59598
$296$		0			0
$297$	6.48370e12	+	1.12301e13i	0.162803	+	0.281983i
$298$		0			0
$299$	1.81876e13	−	3.15019e13i	0.440134	−	0.762334i
$300$		0			0
$301$	3.33105e13	+	3.20971e13i	0.777079	+	0.748773i
$302$		0			0
$303$	−1.89015e13	+	3.27384e13i	−0.425170	+	0.736416i
$304$		0			0
$305$	−1.20152e12	−	2.08109e12i	−0.0260664	−	0.0451483i
$306$		0			0
$307$	−8.11886e13			−1.69916			−0.849580	−	0.527460i	$-0.823144\pi$
$307$	−8.11886e13			−1.69916			−0.849580	+	0.527460i	$0.823144\pi$
$308$		0			0
$309$	−3.34499e13			−0.675496
$310$		0			0
$311$	−4.56233e13	−	7.90218e13i	−0.889210	−	1.54016i	−0.840811	−	0.541329i	$-0.817922\pi$
$311$	−4.56233e13	−	7.90218e13i	−0.889210	−	1.54016i	−0.0483988	−	0.998828i	$-0.515412\pi$
$312$		0			0
$313$	−1.75443e13	+	3.03876e13i	−0.330097	+	0.571745i	−0.982531	−	0.186101i	$-0.940415\pi$
$313$	−1.75443e13	+	3.03876e13i	−0.330097	+	0.571745i	0.652433	+	0.757846i	$0.273748\pi$
$314$		0			0
$315$	−7.00718e12	+	2.82360e13i	−0.127302	+	0.512974i
$316$		0			0
$317$	−3.71054e13	+	6.42684e13i	−0.651045	+	1.12764i	0.331825	+	0.943341i	$0.392336\pi$
$317$	−3.71054e13	+	6.42684e13i	−0.651045	+	1.12764i	−0.982870	+	0.184301i	$0.940998\pi$
$318$		0			0
$319$	7.46496e13	+	1.29297e14i	1.26526	+	2.19149i
$320$		0			0
$321$	4.62669e13			0.757692
$322$		0			0
$323$	−2.15654e13			−0.341305
$324$		0			0
$325$	2.81443e13	+	4.87474e13i	0.430559	+	0.745750i
$326$		0			0
$327$	−2.29792e13	+	3.98012e13i	−0.339878	+	0.588686i
$328$		0			0
$329$	5.92283e12	−	1.70537e12i	0.0847133	−	0.0243916i
$330$		0			0
$331$	−5.12968e12	+	8.88487e12i	−0.0709637	+	0.122913i	−0.899324	−	0.437283i	$-0.855941\pi$
$331$	−5.12968e12	+	8.88487e12i	−0.0709637	+	0.122913i	0.828360	+	0.560196i	$0.189274\pi$
$332$		0			0
$333$	6.40860e12	+	1.11000e13i	0.0857670	+	0.148553i
$334$		0			0
$335$	1.91476e14			2.47953
$336$		0			0
$337$	5.27820e13			0.661487			0.330743	−	0.943721i	$-0.392701\pi$
$337$	5.27820e13			0.661487			0.330743	+	0.943721i	$0.392701\pi$
$338$		0			0
$339$	1.57100e13	+	2.72105e13i	0.190580	+	0.330095i
$340$		0			0
$341$	2.67017e13	−	4.62487e13i	0.313610	−	0.543189i
$342$		0			0
$343$	5.86190e13	−	6.55348e13i	0.666685	−	0.745340i
$344$		0			0
$345$	−6.43167e13	+	1.11400e14i	−0.708466	+	1.22710i
$346$		0			0
$347$	−6.11874e13	−	1.05980e14i	−0.652905	−	1.13086i	−0.982415	−	0.186712i	$-0.940217\pi$
$347$	−6.11874e13	−	1.05980e14i	−0.652905	−	1.13086i	0.329510	−	0.944152i	$-0.393116\pi$
$348$		0			0
$349$	2.45906e13			0.254232			0.127116	−	0.991888i	$-0.459428\pi$
$349$	2.45906e13			0.254232			0.127116	+	0.991888i	$0.459428\pi$
$350$		0			0
$351$	−1.09246e13			−0.109450
$352$		0			0
$353$	2.31490e13	+	4.00952e13i	0.224787	+	0.389343i	0.956256	−	0.292533i	$-0.0944980\pi$
$353$	2.31490e13	+	4.00952e13i	0.224787	+	0.389343i	−0.731468	+	0.681875i	$0.761165\pi$
$354$		0			0
$355$	2.92653e13	−	5.06889e13i	0.275484	−	0.477153i
$356$		0			0
$357$	−4.96649e13	+	1.43001e13i	−0.453288	+	0.130516i
$358$		0			0
$359$	−9.74265e13	+	1.68748e14i	−0.862298	+	1.49354i	0.00740641	+	0.999973i	$0.497642\pi$
$359$	−9.74265e13	+	1.68748e14i	−0.862298	+	1.49354i	−0.869705	+	0.493572i	$0.835691\pi$
$360$		0			0
$361$	4.80807e13	+	8.32781e13i	0.412744	+	0.714893i
$362$		0			0
$363$	1.29130e14			1.07533
$364$		0			0
$365$	1.22998e14			0.993777
$366$		0			0
$367$	−7.70186e13	−	1.33400e14i	−0.603854	−	1.04591i	−0.992231	−	0.124406i	$-0.960298\pi$
$367$	−7.70186e13	−	1.33400e14i	−0.603854	−	1.04591i	0.388377	−	0.921501i	$-0.373036\pi$
$368$		0			0
$369$	1.63055e13	−	2.82419e13i	0.124076	−	0.214906i
$370$		0			0
$371$	5.01923e13	−	2.02254e14i	0.370750	−	1.49397i
$372$		0			0
$373$	−7.42105e13	+	1.28536e14i	−0.532190	+	0.921780i	0.467104	+	0.884203i	$0.345297\pi$
$373$	−7.42105e13	+	1.28536e14i	−0.532190	+	0.921780i	−0.999294	+	0.0375776i	$0.988036\pi$
$374$		0			0
$375$	−3.37947e13	−	5.85342e13i	−0.235330	−	0.407603i
$376$		0			0
$377$	−1.25780e14			−0.850616
$378$		0			0
$379$	−2.63905e14			−1.73353			−0.866766	−	0.498715i	$-0.833805\pi$
$379$	−2.63905e14			−1.73353			−0.866766	+	0.498715i	$0.833805\pi$
$380$		0			0
$381$	−2.36758e12	−	4.10077e12i	−0.0151084	−	0.0261685i
$382$		0			0
$383$	2.31627e13	−	4.01190e13i	0.143614	−	0.248746i	−0.785241	−	0.619190i	$-0.787461\pi$
$383$	2.31627e13	−	4.01190e13i	0.143614	−	0.248746i	0.928855	+	0.370444i	$0.120794\pi$
$384$		0			0
$385$	3.20623e14	+	3.08944e14i	1.93180	+	1.86143i
$386$		0			0
$387$	3.07136e13	−	5.31976e13i	0.179854	−	0.311517i
$388$		0			0
$389$	−3.12486e12	−	5.41242e12i	−0.0177872	−	0.0308084i	0.856995	−	0.515325i	$-0.172329\pi$
$389$	−3.12486e12	−	5.41242e12i	−0.0177872	−	0.0308084i	−0.874782	+	0.484517i	$0.838995\pi$
$390$		0			0
$391$	−2.28517e14			−1.26458
$392$		0			0
$393$	6.69717e12			0.0360356
$394$		0			0
$395$	2.37483e13	+	4.11333e13i	0.124265	+	0.215233i
$396$		0			0
$397$	−4.83142e13	+	8.36827e13i	−0.245882	+	0.425880i	−0.962379	−	0.271710i	$-0.912411\pi$
$397$	−4.83142e13	+	8.36827e13i	−0.245882	+	0.425880i	0.716497	+	0.697590i	$0.245744\pi$
$398$		0			0
$399$	−3.50829e13	−	3.38050e13i	−0.173678	−	0.167352i
$400$		0			0
$401$	−6.00607e13	+	1.04028e14i	−0.289265	+	0.501022i	−0.973635	−	0.228113i	$-0.926744\pi$
$401$	−6.00607e13	+	1.04028e14i	−0.289265	+	0.501022i	0.684369	+	0.729136i	$0.260078\pi$
$402$		0			0
$403$	2.24953e13	+	3.89631e13i	0.105418	+	0.182589i
$404$		0			0
$405$	3.86326e13			0.176178
$406$		0			0
$407$	1.96162e14			0.870654
$408$		0			0
$409$	−1.06240e14	−	1.84013e14i	−0.458998	−	0.795007i	0.539911	−	0.841722i	$-0.318458\pi$
$409$	−1.06240e14	−	1.84013e14i	−0.458998	−	0.795007i	−0.998908	+	0.0467150i	$0.985125\pi$
$410$		0			0
$411$	3.76738e13	−	6.52530e13i	0.158456	−	0.274454i
$412$		0			0
$413$	−9.62931e13	+	3.88021e14i	−0.394339	+	1.58902i
$414$		0			0
$415$	2.55498e14	−	4.42536e14i	1.01888	−	1.76475i
$416$		0			0
$417$	−6.42647e13	−	1.11310e14i	−0.249588	−	0.432300i
$418$		0			0
$419$	7.70399e13			0.291433			0.145716	−	0.989326i	$-0.453451\pi$
$419$	7.70399e13			0.291433			0.145716	+	0.989326i	$0.453451\pi$
$420$		0			0
$421$	−3.49104e14			−1.28648			−0.643241	−	0.765664i	$-0.722411\pi$
$421$	−3.49104e14			−1.28648			−0.643241	+	0.765664i	$0.722411\pi$
$422$		0			0
$423$	−4.09230e12	−	7.08807e12i	−0.0146925	−	0.0254482i
$424$		0			0
$425$	1.76808e14	−	3.06241e14i	0.618534	−	1.07133i
$426$		0			0
$427$	9.26776e12	−	2.66848e12i	0.0315952	−	0.00909726i
$428$		0			0
$429$	−8.35984e13	+	1.44797e14i	−0.277768	+	0.481109i
$430$		0			0
$431$	−3.54794e13	−	6.14522e13i	−0.114908	−	0.199027i	0.802835	−	0.596202i	$-0.203324\pi$
$431$	−3.54794e13	−	6.14522e13i	−0.114908	−	0.199027i	−0.917743	+	0.397174i	$0.869991\pi$
$432$		0			0
$433$	−5.57341e14			−1.75969			−0.879847	−	0.475256i	$-0.842355\pi$
$433$	−5.57341e14			−1.75969			−0.879847	+	0.475256i	$0.842355\pi$
$434$		0			0
$435$	4.44794e14			1.36920
$436$		0			0
$437$	−1.07708e14	−	1.86555e14i	−0.323295	−	0.559963i
$438$		0			0
$439$	1.90654e14	−	3.30223e14i	0.558074	−	0.966613i	−0.439583	−	0.898202i	$-0.644874\pi$
$439$	1.90654e14	−	3.30223e14i	0.558074	−	0.966613i	0.997657	−	0.0684109i	$-0.0217929\pi$
$440$		0			0
$441$	−1.03212e14	−	5.45891e13i	−0.294658	−	0.155845i
$442$		0			0
$443$	6.88095e13	−	1.19182e14i	0.191614	−	0.331886i	−0.754171	−	0.656678i	$-0.771961\pi$
$443$	6.88095e13	−	1.19182e14i	0.191614	−	0.331886i	0.945785	+	0.324792i	$0.105294\pi$
$444$		0			0
$445$	−9.46091e13	−	1.63868e14i	−0.257012	−	0.445157i
$446$		0			0
$447$	−1.07504e14			−0.284926
$448$		0			0
$449$	−1.91960e14			−0.496429			−0.248214	−	0.968705i	$-0.579844\pi$
$449$	−1.91960e14			−0.496429			−0.248214	+	0.968705i	$0.579844\pi$
$450$		0			0
$451$	−2.49548e14	−	4.32230e14i	−0.629772	−	1.09080i
$452$		0			0
$453$	2.12636e14	−	3.68297e14i	0.523717	−	0.907105i
$454$		0			0
$455$	−3.60463e14	+	1.03789e14i	−0.866558	+	0.249509i
$456$		0			0
$457$	3.61232e14	−	6.25673e14i	0.847711	−	1.46828i	−0.0355355	−	0.999368i	$-0.511314\pi$
$457$	3.61232e14	−	6.25673e14i	0.847711	−	1.46828i	0.883246	−	0.468910i	$-0.155353\pi$
$458$		0			0
$459$	3.43153e13	+	5.94359e13i	0.0786173	+	0.136169i
$460$		0			0
$461$	−4.28898e14			−0.959398			−0.479699	−	0.877433i	$-0.659254\pi$
$461$	−4.28898e14			−0.959398			−0.479699	+	0.877433i	$0.659254\pi$
$462$		0			0
$463$	6.20134e14			1.35453			0.677267	−	0.735737i	$-0.263164\pi$
$463$	6.20134e14			1.35453			0.677267	+	0.735737i	$0.263164\pi$
$464$		0			0
$465$	−7.95501e13	−	1.37785e14i	−0.169687	−	0.293907i
$466$		0			0
$467$	−3.53364e14	+	6.12045e14i	−0.736173	+	1.27509i	0.218033	+	0.975941i	$0.430036\pi$
$467$	−3.53364e14	+	6.12045e14i	−0.736173	+	1.27509i	−0.954207	+	0.299148i	$0.903298\pi$
$468$		0			0
$469$	−1.85092e14	+	7.45844e14i	−0.376650	+	1.51774i
$470$		0			0
$471$	−1.69579e14	+	2.93719e14i	−0.337099	+	0.583872i
$472$		0			0
$473$	−4.70059e14	−	8.14167e14i	−0.912886	−	1.58116i
$474$		0			0
$475$	3.33343e14			0.632523
$476$		0			0
$477$	−2.76725e14			−0.513094
$478$		0			0
$479$	7.76957e13	+	1.34573e14i	0.140783	+	0.243844i	0.927792	−	0.373098i	$-0.121705\pi$
$479$	7.76957e13	+	1.34573e14i	0.140783	+	0.243844i	−0.787008	+	0.616942i	$0.788371\pi$
$480$		0			0
$481$	−8.26301e13	+	1.43120e14i	−0.146332	+	0.253455i
$482$		0			0
$483$	−3.71755e14	−	3.58214e14i	−0.643499	−	0.620059i
$484$		0			0
$485$	−8.72045e14	+	1.51043e15i	−1.47557	+	2.55576i
$486$		0			0
$487$	−1.67311e14	−	2.89791e14i	−0.276767	−	0.479375i	0.693812	−	0.720156i	$-0.255930\pi$
$487$	−1.67311e14	−	2.89791e14i	−0.276767	−	0.479375i	−0.970579	+	0.240781i	$0.922596\pi$
$488$		0			0
$489$	−3.32091e14			−0.537104
$490$		0			0
$491$	5.46129e14			0.863668			0.431834	−	0.901953i	$-0.357867\pi$
$491$	5.46129e14			0.863668			0.431834	+	0.901953i	$0.357867\pi$
$492$		0			0
$493$	3.95087e14	+	6.84311e14i	0.610991	+	1.05827i
$494$		0			0
$495$	2.95628e14	−	5.12043e14i	0.447113	−	0.774422i
$496$		0			0
$497$	1.69155e14	+	1.62994e14i	0.250222	+	0.241108i
$498$		0			0
$499$	3.26652e14	−	5.65778e14i	0.472642	−	0.818640i	−0.526868	−	0.849947i	$-0.676634\pi$
$499$	3.26652e14	−	5.65778e14i	0.472642	−	0.818640i	0.999510	+	0.0313069i	$0.00996694\pi$
$500$		0			0
$501$	−7.53363e13	−	1.30486e14i	−0.106634	−	0.184696i
$502$		0			0
$503$	−1.29756e15			−1.79682			−0.898409	−	0.439161i	$-0.855276\pi$
$503$	−1.29756e15			−1.79682			−0.898409	+	0.439161i	$0.855276\pi$
$504$		0			0
$505$	1.72365e15			2.33532
$506$		0			0
$507$	1.47319e14	+	2.55163e14i	0.195305	+	0.338278i
$508$		0			0
$509$	5.20168e14	−	9.00957e14i	0.674832	−	1.16884i	−0.301686	−	0.953407i	$-0.597549\pi$
$509$	5.20168e14	−	9.00957e14i	0.674832	−	1.16884i	0.976518	−	0.215436i	$-0.0691172\pi$
$510$		0			0
$511$	−1.18897e14	+	4.79107e14i	−0.150959	+	0.608300i
$512$		0			0
$513$	−3.23479e13	+	5.60282e13i	−0.0401977	+	0.0696244i
$514$		0			0
$515$	7.62583e14	+	1.32083e15i	0.927572	+	1.60660i
$516$		0			0
$517$	−1.25262e14			−0.149149
$518$		0			0
$519$	1.93963e14			0.226099
$520$		0			0
$521$	8.26924e14	+	1.43227e15i	0.943752	+	1.63463i	0.758231	+	0.651986i	$0.226064\pi$
$521$	8.26924e14	+	1.43227e15i	0.943752	+	1.63463i	0.185522	+	0.982640i	$0.440603\pi$
$522$		0			0
$523$	−2.37190e14	+	4.10824e14i	−0.265055	+	0.459089i	−0.967578	−	0.252572i	$-0.918724\pi$
$523$	−2.37190e14	+	4.10824e14i	−0.265055	+	0.459089i	0.702523	+	0.711661i	$0.252057\pi$
$524$		0			0
$525$	7.67686e14	−	2.21041e14i	0.840055	−	0.241878i
$526$		0			0
$527$	1.41320e14	−	2.44774e14i	0.151442	−	0.262305i
$528$		0			0
$529$	−6.64915e14	−	1.15167e15i	−0.697847	−	1.20871i
$530$		0			0
$531$	5.30892e14			0.545740
$532$		0			0
$533$	4.20473e14			0.423388
$534$		0			0
$535$	−1.05478e15	−	1.82694e15i	−1.04044	−	1.80210i
$536$		0			0
$537$	9.68775e13	−	1.67797e14i	0.0936191	−	0.162153i
$538$		0			0
$539$	−1.51334e15	+	9.50257e14i	−1.43284	+	0.899711i
$540$		0			0
$541$	−2.57042e14	+	4.45210e14i	−0.238462	+	0.413028i	−0.960273	−	0.279062i	$-0.909977\pi$
$541$	−2.57042e14	+	4.45210e14i	−0.238462	+	0.413028i	0.721811	+	0.692090i	$0.243310\pi$
$542$		0			0
$543$	−4.72846e14	−	8.18993e14i	−0.429853	−	0.744528i
$544$		0			0
$545$	2.09550e15			1.86684
$546$		0			0
$547$	4.36242e14			0.380888			0.190444	−	0.981698i	$-0.439007\pi$
$547$	4.36242e14			0.380888			0.190444	+	0.981698i	$0.439007\pi$
$548$		0			0
$549$	−6.40344e12	−	1.10911e13i	−0.00547981	−	0.00949131i
$550$		0			0
$551$	−3.72435e14	+	6.45077e14i	−0.312404	+	0.541100i
$552$		0			0
$553$	−1.83180e14	+	5.27433e13i	−0.150623	+	0.0433689i
$554$		0			0
$555$	2.92204e14	−	5.06112e14i	0.235545	−	0.407977i
$556$		0			0
$557$	1.08792e15	+	1.88434e15i	0.859795	+	1.48921i	0.872124	+	0.489285i	$0.162742\pi$
$557$	1.08792e15	+	1.88434e15i	0.859795	+	1.48921i	−0.0123289	+	0.999924i	$0.503925\pi$
$558$		0			0
$559$	7.92020e14			0.613721
$560$		0			0
$561$	1.05036e15			0.798075
$562$		0			0
$563$	−4.45391e14	−	7.71439e14i	−0.331852	−	0.574785i	0.651023	−	0.759058i	$-0.274340\pi$
$563$	−4.45391e14	−	7.71439e14i	−0.331852	−	0.574785i	−0.982875	+	0.184273i	$0.941007\pi$
$564$		0			0
$565$	7.16307e14	−	1.24068e15i	0.523399	−	0.906554i
$566$		0			0
$567$	−3.73445e13	+	1.50483e14i	−0.0267621	+	0.107840i
$568$		0			0
$569$	−1.25020e15	+	2.16542e15i	−0.878747	+	1.52203i	−0.0260291	+	0.999661i	$0.508286\pi$
$569$	−1.25020e15	+	2.16542e15i	−0.878747	+	1.52203i	−0.852717	+	0.522372i	$0.825047\pi$
$570$		0			0
$571$	1.20063e15	+	2.07955e15i	0.827773	+	1.43374i	0.899782	+	0.436341i	$0.143726\pi$
$571$	1.20063e15	+	2.07955e15i	0.827773	+	1.43374i	−0.0720088	+	0.997404i	$0.522941\pi$
$572$		0			0
$573$	7.99135e14			0.540467
$574$		0			0
$575$	3.53226e15			2.34358
$576$		0			0
$577$	−8.01843e14	−	1.38883e15i	−0.521942	−	0.904031i	−0.999674	−	0.0255249i	$-0.991874\pi$
$577$	−8.01843e14	−	1.38883e15i	−0.521942	−	0.904031i	0.477732	−	0.878506i	$-0.341459\pi$
$578$		0			0
$579$	−4.24719e14	+	7.35635e14i	−0.271250	+	0.469819i
$580$		0			0
$581$	1.47680e15	+	1.42301e15i	0.925449	+	0.891739i
$582$		0			0
$583$	−2.11758e15	+	3.66775e15i	−1.30215	+	2.25540i
$584$		0			0
$585$	2.49057e14	+	4.31380e14i	0.150294	+	0.260317i
$586$		0			0
$587$	−2.58598e15			−1.53150			−0.765749	−	0.643140i	$-0.777631\pi$
$587$	−2.58598e15			−1.53150			−0.765749	+	0.643140i	$0.777631\pi$
$588$		0			0
$589$	2.66436e14			0.154867
$590$		0			0
$591$	−6.79112e14	−	1.17626e15i	−0.387445	−	0.671074i
$592$		0			0
$593$	−7.43649e14	+	1.28804e15i	−0.416454	+	0.721320i	−0.995580	−	0.0939186i	$-0.970061\pi$
$593$	−7.43649e14	+	1.28804e15i	−0.416454	+	0.721320i	0.579126	+	0.815238i	$0.303394\pi$
$594$		0			0
$595$	1.69692e15	+	1.63510e15i	0.932861	+	0.898881i
$596$		0			0
$597$	6.55954e14	−	1.13615e15i	0.354009	−	0.613162i
$598$		0			0
$599$	−5.28520e14	−	9.15423e14i	−0.280036	−	0.485036i	0.691357	−	0.722513i	$-0.257013\pi$
$599$	−5.28520e14	−	9.15423e14i	−0.280036	−	0.485036i	−0.971393	+	0.237477i	$0.923680\pi$
$600$		0			0
$601$	−2.15911e15			−1.12322			−0.561610	−	0.827402i	$-0.689818\pi$
$601$	−2.15911e15			−1.12322			−0.561610	+	0.827402i	$0.689818\pi$
$602$		0			0
$603$	1.02047e15			0.521259
$604$		0			0
$605$	−2.94388e15	−	5.09894e15i	−1.47661	−	2.55756i
$606$		0			0
$607$	−9.50659e14	+	1.64659e15i	−0.468260	+	0.811050i	−0.999342	−	0.0362702i	$-0.988452\pi$
$607$	−9.50659e14	+	1.64659e15i	−0.468260	+	0.811050i	0.531082	+	0.847320i	$0.321786\pi$
$608$		0			0
$609$	−4.29964e14	+	1.73257e15i	−0.207987	+	0.838101i
$610$		0			0
$611$	5.27646e13	−	9.13909e13i	0.0250678	−	0.0434187i
$612$		0			0
$613$	−4.85740e14	−	8.41326e14i	−0.226658	−	0.392583i	0.730158	−	0.683279i	$-0.239447\pi$
$613$	−4.85740e14	−	8.41326e14i	−0.226658	−	0.392583i	−0.956816	+	0.290696i	$0.906113\pi$
$614$		0			0
$615$	−1.48691e15			−0.681511
$616$		0			0
$617$	−1.39104e15			−0.626282			−0.313141	−	0.949707i	$-0.601381\pi$
$617$	−1.39104e15			−0.626282			−0.313141	+	0.949707i	$0.601381\pi$
$618$		0			0
$619$	−1.56881e15	−	2.71726e15i	−0.693859	−	1.20180i	−0.970564	−	0.240844i	$-0.922576\pi$
$619$	−1.56881e15	−	2.71726e15i	−0.693859	−	1.20180i	0.276705	−	0.960955i	$-0.410758\pi$
$620$		0			0
$621$	−3.42774e14	+	5.93701e14i	−0.148937	+	0.257967i
$622$		0			0
$623$	7.29757e14	−	2.10120e14i	0.311526	−	0.0896979i
$624$		0			0
$625$	2.64095e14	−	4.57426e14i	0.110769	−	0.191858i
$626$		0			0
$627$	4.95071e14	+	8.57489e14i	0.204031	+	0.353392i
$628$		0			0
$629$	1.03820e15			0.420438
$630$		0			0
$631$	4.42265e15			1.76003			0.880017	−	0.474942i	$-0.157531\pi$
$631$	4.42265e15			1.76003			0.880017	+	0.474942i	$0.157531\pi$
$632$		0			0
$633$	−9.74888e14	−	1.68855e15i	−0.381271	−	0.660381i
$634$		0			0
$635$	−1.07951e14	+	1.86977e14i	−0.0414927	+	0.0718675i
$636$		0			0
$637$	−5.58354e13	−	1.50441e15i	−0.0210932	−	0.568329i
$638$		0			0
$639$	1.55968e14	−	2.70145e14i	0.0579137	−	0.100310i
$640$		0			0
$641$	−4.94254e14	−	8.56073e14i	−0.180398	−	0.312458i	0.761618	−	0.648026i	$-0.224405\pi$
$641$	−4.94254e14	−	8.56073e14i	−0.180398	−	0.312458i	−0.942016	+	0.335568i	$0.891072\pi$
$642$		0			0
$643$	2.69033e15			0.965262			0.482631	−	0.875824i	$-0.339681\pi$
$643$	2.69033e15			0.965262			0.482631	+	0.875824i	$0.339681\pi$
$644$		0			0
$645$	−2.80081e15			−0.987883
$646$		0			0
$647$	−1.47451e15	−	2.55393e15i	−0.511299	−	0.885595i	−0.999914	−	0.0130960i	$-0.995831\pi$
$647$	−1.47451e15	−	2.55393e15i	−0.511299	−	0.885595i	0.488616	−	0.872499i	$-0.337502\pi$
$648$		0			0
$649$	4.06254e15	−	7.03652e15i	1.38501	−	2.39890i
$650$		0			0
$651$	6.13600e14	−	1.76675e14i	0.205679	−	0.0592214i
$652$		0			0
$653$	1.17965e15	−	2.04321e15i	0.388803	−	0.673427i	−0.603486	−	0.797374i	$-0.706222\pi$
$653$	1.17965e15	−	2.04321e15i	0.388803	−	0.673427i	0.992289	+	0.123947i	$0.0395553\pi$
$654$		0			0
$655$	−1.52681e14	−	2.64451e14i	−0.0494831	−	0.0857072i
$656$		0			0
$657$	6.55516e14			0.208917
$658$		0			0
$659$	−4.40458e14			−0.138050			−0.0690248	−	0.997615i	$-0.521989\pi$
$659$	−4.40458e14			−0.138050			−0.0690248	+	0.997615i	$0.521989\pi$
$660$		0			0
$661$	7.68645e14	+	1.33133e15i	0.236929	+	0.410373i	0.959831	−	0.280577i	$-0.0905259\pi$
$661$	7.68645e14	+	1.33133e15i	0.236929	+	0.410373i	−0.722903	+	0.690950i	$0.757193\pi$
$662$		0			0
$663$	−4.42449e14	+	7.66344e14i	−0.134134	+	0.232327i
$664$		0			0
$665$	−5.35043e14	+	2.15600e15i	−0.159540	+	0.642879i
$666$		0			0
$667$	−3.94650e15	+	6.83554e15i	−1.15750	+	2.00484i
$668$		0			0
$669$	−3.46873e12	−	6.00802e12i	−0.00100075	−	0.00173336i
$670$		0			0
$671$	−1.96004e14			−0.0556277
$672$		0			0
$673$	−3.83410e14			−0.107048			−0.0535242	−	0.998567i	$-0.517045\pi$
$673$	−3.83410e14			−0.107048			−0.0535242	+	0.998567i	$0.517045\pi$
$674$		0			0
$675$	−5.30423e14	−	9.18719e14i	−0.145697	−	0.252355i
$676$		0			0
$677$	1.52818e15	−	2.64688e15i	0.412986	−	0.715313i	−0.582228	−	0.813025i	$-0.697819\pi$
$677$	1.52818e15	−	2.64688e15i	0.412986	−	0.715313i	0.995215	+	0.0977120i	$0.0311524\pi$
$678$		0			0
$679$	−5.04048e15	−	4.85688e15i	−1.34026	−	1.29144i
$680$		0			0
$681$	−1.68540e15	+	2.91920e15i	−0.440956	+	0.763757i
$682$		0			0
$683$	−1.24318e15	−	2.15324e15i	−0.320051	−	0.554344i	0.660447	−	0.750872i	$-0.270367\pi$
$683$	−1.24318e15	−	2.15324e15i	−0.320051	−	0.554344i	−0.980498	+	0.196528i	$0.937033\pi$
$684$		0			0
$685$	−3.43552e15			−0.870350
$686$		0			0
$687$	1.41669e15			0.353193
$688$		0			0
$689$	−1.78399e15	−	3.08997e15i	−0.437711	−	0.758137i
$690$		0			0
$691$	1.75214e15	−	3.03479e15i	0.423096	−	0.732823i	−0.573145	−	0.819454i	$-0.694277\pi$
$691$	1.75214e15	−	3.03479e15i	0.423096	−	0.732823i	0.996240	+	0.0866310i	$0.0276101\pi$
$692$		0			0
$693$	1.70875e15	+	1.64651e15i	0.406112	+	0.391319i
$694$		0			0
$695$	−2.93019e15	+	5.07523e15i	−0.685455	+	1.18724i
$696$		0			0
$697$	−1.32075e15	−	2.28760e15i	−0.304116	−	0.526745i
$698$		0			0
$699$	−3.73594e15			−0.846789
$700$		0			0
$701$	5.93387e15			1.32400			0.662001	−	0.749503i	$-0.269707\pi$
$701$	5.93387e15			1.32400			0.662001	+	0.749503i	$0.269707\pi$
$702$		0			0
$703$	4.89337e14	+	8.47557e14i	0.107487	+	0.186172i
$704$		0			0
$705$	−1.86591e14	+	3.23185e14i	−0.0403506	+	0.0698893i
$706$		0			0
$707$	−1.66618e15	+	6.71402e15i	−0.354745	+	1.42947i
$708$		0			0
$709$	−2.66852e15	+	4.62202e15i	−0.559393	+	0.968896i	0.438155	+	0.898900i	$0.355632\pi$
$709$	−2.66852e15	+	4.62202e15i	−0.559393	+	0.968896i	−0.997547	+	0.0699967i	$0.977701\pi$
$710$		0			0
$711$	1.26566e14	+	2.19219e14i	0.0261236	+	0.0452475i
$712$		0			0
$713$	2.82328e15			0.573801
$714$		0			0
$715$	7.62343e15			1.52569
$716$		0			0
$717$	−2.10174e15	−	3.64032e15i	−0.414213	−	0.717438i
$718$		0			0
$719$	1.51335e15	−	2.62120e15i	0.293718	−	0.508735i	−0.680968	−	0.732313i	$-0.738441\pi$
$719$	1.51335e15	−	2.62120e15i	0.293718	−	0.508735i	0.974686	+	0.223579i	$0.0717740\pi$
$720$		0			0
$721$	−5.88210e15	+	1.69364e15i	−1.12432	+	0.323726i
$722$		0			0
$723$	4.36579e14	−	7.56176e14i	0.0821868	−	0.142352i
$724$		0			0
$725$	−6.10699e15	−	1.05776e16i	−1.13232	−	1.96123i
$726$		0			0
$727$	−1.66738e15			−0.304506			−0.152253	−	0.988342i	$-0.548653\pi$
$727$	−1.66738e15			−0.304506			−0.152253	+	0.988342i	$0.548653\pi$
$728$		0			0
$729$	2.05891e14			0.0370370
$730$		0			0
$731$	−2.48781e15	−	4.30902e15i	−0.440831	−	0.763542i
$732$		0			0
$733$	−2.19667e15	+	3.80474e15i	−0.383436	+	0.664130i	−0.991551	−	0.129719i	$-0.958593\pi$
$733$	−2.19667e15	+	3.80474e15i	−0.383436	+	0.664130i	0.608115	+	0.793849i	$0.291926\pi$
$734$		0			0
$735$	1.97450e14	+	5.32004e15i	0.0339529	+	0.914817i
$736$		0			0
$737$	7.80891e15	−	1.35254e16i	1.32288	−	2.29129i
$738$		0			0
$739$	−9.77656e14	−	1.69335e15i	−0.163170	−	0.282620i	0.772834	−	0.634609i	$-0.218839\pi$
$739$	−9.77656e14	−	1.69335e15i	−0.163170	−	0.282620i	−0.936004	+	0.351989i	$0.885505\pi$
$740$		0			0
$741$	−8.34164e14			−0.137167
$742$		0			0
$743$	7.66464e15			1.24180			0.620902	−	0.783888i	$-0.286766\pi$
$743$	7.66464e15			1.24180			0.620902	+	0.783888i	$0.286766\pi$
$744$		0			0
$745$	2.45085e15	+	4.24499e15i	0.391252	+	0.677668i
$746$		0			0
$747$	1.36167e15	−	2.35848e15i	0.214195	−	0.370996i
$748$		0			0
$749$	8.13595e15	−	2.34259e15i	1.26113	−	0.363117i
$750$		0			0
$751$	−4.89846e15	+	8.48439e15i	−0.748239	+	1.29599i	0.200427	+	0.979709i	$0.435767\pi$
$751$	−4.89846e15	+	8.48439e15i	−0.748239	+	1.29599i	−0.948666	+	0.316279i	$0.897566\pi$
$752$		0			0
$753$	2.52547e14	+	4.37424e14i	0.0380163	+	0.0658461i
$754$		0			0
$755$	−1.93905e16			−2.87661
$756$		0			0
$757$	1.58148e15			0.231226			0.115613	−	0.993294i	$-0.463117\pi$
$757$	1.58148e15			0.231226			0.115613	+	0.993294i	$0.463117\pi$
$758$		0			0
$759$	5.24601e15	+	9.08635e15i	0.755961	+	1.30936i
$760$		0			0
$761$	3.93379e15	−	6.81352e15i	0.558722	−	0.967734i	−0.438882	−	0.898545i	$-0.644625\pi$
$761$	3.93379e15	−	6.81352e15i	0.558722	−	0.967734i	0.997604	−	0.0691896i	$-0.0220413\pi$
$762$		0			0
$763$	−2.02564e15	+	8.16246e15i	−0.283580	+	1.14271i
$764$		0			0
$765$	1.56463e15	−	2.71001e15i	0.215910	−	0.373967i
$766$		0			0
$767$	3.42256e15	+	5.92804e15i	0.465561	+	0.806375i
$768$		0			0
$769$	6.27927e15			0.842005			0.421002	−	0.907060i	$-0.361678\pi$
$769$	6.27927e15			0.842005			0.421002	+	0.907060i	$0.361678\pi$
$770$		0			0
$771$	−2.32164e15			−0.306900
$772$		0			0
$773$	1.66695e15	+	2.88725e15i	0.217238	+	0.376268i	0.953963	−	0.299925i	$-0.0969618\pi$
$773$	1.66695e15	+	2.88725e15i	0.217238	+	0.376268i	−0.736724	+	0.676193i	$0.763628\pi$
$774$		0			0
$775$	−2.18443e15	+	3.78355e15i	−0.280659	+	0.486116i
$776$		0			0
$777$	1.68896e15	+	1.62744e15i	0.213946	+	0.206153i
$778$		0			0
$779$	1.24503e15	−	2.15645e15i	0.155497	−	0.269329i
$780$		0			0
$781$	−2.38703e15	−	4.13446e15i	−0.293952	−	0.509140i
$782$		0			0
$783$	2.37051e15			0.287841
$784$		0			0
$785$	1.54641e16			1.85158
$786$		0			0
$787$	−4.18067e15	−	7.24113e15i	−0.493611	−	0.854960i	0.506362	−	0.862321i	$-0.330990\pi$
$787$	−4.18067e15	−	7.24113e15i	−0.493611	−	0.854960i	−0.999973	+	0.00736161i	$0.997657\pi$
$788$		0			0
$789$	−3.94837e15	+	6.83877e15i	−0.459721	+	0.796259i
$790$		0			0
$791$	4.14031e15	+	3.98949e15i	0.475403	+	0.458086i
$792$		0			0
$793$	8.25635e13	−	1.43004e14i	0.00934944	−	0.0161937i
$794$		0			0
$795$	6.30871e15	+	1.09270e16i	0.704566	+	1.22034i
$796$		0			0
$797$	−5.02626e15			−0.553636			−0.276818	−	0.960922i	$-0.589280\pi$
$797$	−5.02626e15			−0.553636			−0.276818	+	0.960922i	$0.589280\pi$
$798$		0			0
$799$	−6.62955e14			−0.0720240
$800$		0			0
$801$	−5.04216e14	−	8.73327e14i	−0.0540303	−	0.0935833i
$802$		0			0
$803$	5.01620e15	−	8.68831e15i	0.530199	−	0.918332i
$804$		0			0
$805$	−5.66956e15	+	2.28460e16i	−0.591115	+	2.38195i
$806$		0			0
$807$	1.35561e15	−	2.34798e15i	0.139421	−	0.241485i
$808$		0			0
$809$	3.22897e15	+	5.59275e15i	0.327603	+	0.567425i	0.982036	−	0.188695i	$-0.0604258\pi$
$809$	3.22897e15	+	5.59275e15i	0.327603	+	0.567425i	−0.654433	+	0.756120i	$0.727093\pi$
$810$		0			0
$811$	6.75664e15			0.676264			0.338132	−	0.941099i	$-0.390205\pi$
$811$	6.75664e15			0.676264			0.338132	+	0.941099i	$0.390205\pi$
$812$		0			0
$813$	3.31131e15			0.326966
$814$		0			0
$815$	7.57094e15	+	1.31133e16i	0.737536	+	1.27745i
$816$		0			0
$817$	2.34518e15	−	4.06197e15i	0.225401	−	0.390405i
$818$		0			0
$819$	−1.92107e15	+	5.53137e14i	−0.182172	+	0.0524531i
$820$		0			0
$821$	−1.36313e15	+	2.36101e15i	−0.127541	+	0.220907i	−0.922723	−	0.385463i	$-0.874042\pi$
$821$	−1.36313e15	+	2.36101e15i	−0.127541	+	0.220907i	0.795182	+	0.606370i	$0.207375\pi$
$822$		0			0
$823$	−2.57340e15	−	4.45726e15i	−0.237579	−	0.411499i	0.722440	−	0.691434i	$-0.243021\pi$
$823$	−2.57340e15	−	4.45726e15i	−0.237579	−	0.411499i	−0.960019	+	0.279934i	$0.909687\pi$
$824$		0			0
$825$	−1.62358e16			−1.47903
$826$		0			0
$827$	−1.44595e16			−1.29979			−0.649896	−	0.760023i	$-0.725188\pi$
$827$	−1.44595e16			−1.29979			−0.649896	+	0.760023i	$0.725188\pi$
$828$		0			0
$829$	5.58791e15	+	9.67854e15i	0.495677	+	0.858538i	0.999988	−	0.00498412i	$-0.00158650\pi$
$829$	5.58791e15	+	9.67854e15i	0.495677	+	0.858538i	−0.504310	+	0.863523i	$0.668253\pi$
$830$		0			0
$831$	2.78889e15	−	4.83049e15i	0.244132	−	0.422850i
$832$		0			0
$833$	−8.00944e15	+	5.02929e15i	−0.691918	+	0.434469i
$834$		0			0
$835$	−3.43500e15	+	5.94960e15i	−0.292854	+	0.507238i
$836$		0			0
$837$	−4.23959e14	−	7.34319e14i	−0.0356725	−	0.0617867i
$838$		0			0
$839$	4.90990e15			0.407739			0.203869	−	0.978998i	$-0.434648\pi$
$839$	4.90990e15			0.407739			0.203869	+	0.978998i	$0.434648\pi$
$840$		0			0
$841$	1.50922e16			1.23702
$842$		0			0
$843$	1.61034e15	+	2.78919e15i	0.130276	+	0.225645i
$844$		0			0
$845$	6.71707e15	−	1.16343e16i	0.536375	−	0.929028i
$846$		0			0
$847$	2.27073e16	−	6.53813e15i	1.78981	−	0.515341i
$848$		0			0
$849$	−5.74068e15	+	9.94315e15i	−0.446654	+	0.773627i
$850$		0			0
$851$	5.18525e15	+	8.98111e15i	0.398251	+	0.689791i
$852$		0			0
$853$	1.08977e16			0.826259			0.413130	−	0.910672i	$-0.364436\pi$
$853$	1.08977e16			0.826259			0.413130	+	0.910672i	$0.364436\pi$
$854$		0			0
$855$	2.94984e15			0.220793
$856$		0			0
$857$	−7.46459e15	−	1.29291e16i	−0.551584	−	0.955372i	−0.998161	−	0.0606261i	$-0.980690\pi$
$857$	−7.46459e15	−	1.29291e16i	−0.551584	−	0.955372i	0.446577	−	0.894745i	$-0.352643\pi$
$858$		0			0
$859$	9.26814e15	−	1.60529e16i	0.676130	−	1.17109i	−0.300007	−	0.953937i	$-0.596989\pi$
$859$	9.26814e15	−	1.60529e16i	0.676130	−	1.17109i	0.976137	−	0.217155i	$-0.0696776\pi$
$860$		0			0
$861$	1.43734e15	−	5.79187e15i	0.103524	−	0.417159i
$862$		0			0
$863$	8.01520e15	−	1.38827e16i	0.569974	−	0.987223i	−0.426594	−	0.904443i	$-0.640287\pi$
$863$	8.01520e15	−	1.38827e16i	0.569974	−	0.987223i	0.996568	−	0.0827802i	$-0.0263799\pi$
$864$		0			0
$865$	−4.42194e15	−	7.65902e15i	−0.310473	−	0.537755i
$866$		0			0
$867$	−2.76897e15			−0.191961
$868$		0			0
$869$	3.87408e15			0.265191
$870$		0			0
$871$	6.57875e15	+	1.13947e16i	0.444676	+	0.770202i
$872$		0			0
$873$	−4.64753e15	+	8.04976e15i	−0.310202	+	0.537285i
$874$		0			0
$875$	−8.90645e15	−	8.58203e15i	−0.587030	−	0.565647i
$876$		0			0
$877$	−3.71479e13	+	6.43421e13i	−0.00241789	+	0.00418791i	−0.867232	−	0.497905i	$-0.834103\pi$
$877$	−3.71479e13	+	6.43421e13i	−0.00241789	+	0.00418791i	0.864814	+	0.502092i	$0.167436\pi$
$878$		0			0
$879$	−5.47157e15	−	9.47704e15i	−0.351701	−	0.609164i
$880$		0			0
$881$	3.09340e14			0.0196367			0.00981834	−	0.999952i	$-0.496875\pi$
$881$	3.09340e14			0.0196367			0.00981834	+	0.999952i	$0.496875\pi$
$882$		0			0
$883$	−1.33039e16			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$883$	−1.33039e16			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$884$		0			0
$885$	−1.21032e16	−	2.09633e16i	−0.749395	−	1.29799i
$886$		0			0
$887$	−4.87138e15	+	8.43749e15i	−0.297901	+	0.515980i	−0.975656	−	0.219308i	$-0.929620\pi$
$887$	−4.87138e15	+	8.43749e15i	−0.297901	+	0.515980i	0.677754	+	0.735288i	$0.262953\pi$
$888$		0			0
$889$	−6.23966e14	−	6.01237e14i	−0.0376878	−	0.0363150i
$890$		0			0
$891$	1.57554e15	−	2.72891e15i	0.0939944	−	0.162803i
$892$		0			0
$893$	−3.12473e14	−	5.41219e14i	−0.0184132	−	0.0318926i
$894$		0			0
$895$	−8.83437e15			−0.514220
$896$		0			0
$897$	−8.83919e15			−0.508223
$898$		0			0
$899$	−4.88122e15	−	8.45453e15i	−0.277236	−	0.480188i
$900$		0			0
$901$	−1.12074e16	+	1.94118e16i	−0.628809	+	1.08913i
$902$		0			0
$903$	2.70743e15	−	1.09098e16i	0.150063	−	0.604692i
$904$		0			0
$905$	−2.15597e16	+	3.73424e16i	−1.18052	+	2.04473i
$906$		0			0
$907$	−1.21611e15	−	2.10636e15i	−0.0657857	−	0.113944i	0.831257	−	0.555889i	$-0.187622\pi$
$907$	−1.21611e15	−	2.10636e15i	−0.0657857	−	0.113944i	−0.897042	+	0.441945i	$0.854289\pi$
$908$		0			0
$909$	9.18614e15			0.490944
$910$		0			0
$911$	−5.60045e15			−0.295714			−0.147857	−	0.989009i	$-0.547238\pi$
$911$	−5.60045e15			−0.295714			−0.147857	+	0.989009i	$0.547238\pi$
$912$		0			0
$913$	−2.08398e16	−	3.60956e16i	−1.08719	−	1.88306i
$914$		0			0
$915$	−2.91969e14	+	5.05704e14i	−0.0150494	+	0.0260664i
$916$		0			0
$917$	1.17769e15	−	3.39092e14i	0.0599788	−	0.0172698i
$918$		0			0
$919$	−3.67446e15	+	6.36435e15i	−0.184909	+	0.320272i	−0.943546	−	0.331242i	$-0.892532\pi$
$919$	−3.67446e15	+	6.36435e15i	−0.184909	+	0.320272i	0.758637	+	0.651514i	$0.225866\pi$
$920$		0			0
$921$	9.86442e15	+	1.70857e16i	0.490505	+	0.849580i
$922$		0			0
$923$	4.02199e15			0.197620
$924$		0			0
$925$	−1.60478e16			−0.779175
$926$		0			0
$927$	4.06416e15	+	7.03933e15i	0.194999	+	0.337748i
$928$		0			0
$929$	−1.59318e16	+	2.75947e16i	−0.755404	+	1.30840i	0.189769	+	0.981829i	$0.439226\pi$
$929$	−1.59318e16	+	2.75947e16i	−0.755404	+	1.30840i	−0.945173	+	0.326569i	$0.894107\pi$
$930$		0			0
$931$	−7.88089e15	−	4.16822e15i	−0.369277	−	0.195312i
$932$		0			0
$933$	−1.10865e16	+	1.92023e16i	−0.513386	+	0.889210i
$934$		0			0
$935$	−2.39460e16	−	4.14756e16i	−1.09589	−	1.89814i
$936$		0			0
$937$	6.96022e14			0.0314815			0.0157407	−	0.999876i	$-0.494989\pi$
$937$	6.96022e14			0.0314815			0.0157407	+	0.999876i	$0.494989\pi$
$938$		0			0
$939$	8.52652e15			0.381163
$940$		0			0
$941$	−2.00499e15	−	3.47274e15i	−0.0885866	−	0.153437i	0.818327	−	0.574753i	$-0.194902\pi$
$941$	−2.00499e15	−	3.47274e15i	−0.0885866	−	0.153437i	−0.906914	+	0.421316i	$0.861568\pi$
$942$		0			0
$943$	1.31929e16	−	2.28507e16i	0.576136	−	0.997897i
$944$		0			0
$945$	6.79347e15	−	1.95605e15i	0.293236	−	0.0844317i
$946$		0			0
$947$	−1.41225e16	+	2.44609e16i	−0.602542	+	1.04363i	0.389893	+	0.920860i	$0.372512\pi$
$947$	−1.41225e16	+	2.44609e16i	−0.602542	+	1.04363i	−0.992435	+	0.122773i	$0.960821\pi$
$948$		0			0
$949$	4.22599e15	+	7.31962e15i	0.178223	+	0.308691i
$950$		0			0
$951$	1.80332e16			0.751762
$952$		0			0
$953$	1.94290e16			0.800645			0.400322	−	0.916374i	$-0.368898\pi$
$953$	1.94290e16			0.800645			0.400322	+	0.916374i	$0.368898\pi$
$954$		0			0
$955$	−1.82185e16	−	3.15554e16i	−0.742154	−	1.28545i
$956$		0			0
$957$	1.81399e16	−	3.14191e16i	0.730496	−	1.26526i
$958$		0			0
$959$	3.32097e15	−	1.33821e16i	0.132210	−	0.532749i
$960$		0			0
$961$	1.09583e16	−	1.89803e16i	0.431283	−	0.747005i
$962$		0			0
$963$	−5.62143e15	−	9.73660e15i	−0.218727	−	0.378846i
$964$		0			0
$965$	3.87306e16			1.48989
$966$		0			0
$967$	−8.43128e14			−0.0320662			−0.0160331	−	0.999871i	$-0.505104\pi$
$967$	−8.43128e14			−0.0320662			−0.0160331	+	0.999871i	$0.505104\pi$
$968$		0			0
$969$	2.62019e15	+	4.53831e15i	0.0985263	+	0.170653i
$970$		0			0
$971$	1.41094e16	−	2.44382e16i	0.524569	−	0.908580i	−0.475022	−	0.879974i	$-0.657560\pi$
$971$	1.41094e16	−	2.44382e16i	0.524569	−	0.908580i	0.999591	−	0.0286063i	$-0.00910690\pi$
$972$		0			0
$973$	−1.69367e16	−	1.63198e16i	−0.622599	−	0.599920i
$974$		0			0
$975$	6.83907e15	−	1.18456e16i	0.248583	−	0.430559i
$976$		0			0
$977$	1.52194e16	+	2.63608e16i	0.546988	+	0.947411i	0.998479	+	0.0551353i	$0.0175590\pi$
$977$	1.52194e16	+	2.63608e16i	0.546988	+	0.947411i	−0.451491	+	0.892276i	$0.649108\pi$
$978$		0			0
$979$	−1.54336e16			−0.548483
$980$		0			0
$981$	1.11679e16			0.392457
$982$		0			0
$983$	−5.50449e15	−	9.53406e15i	−0.191282	−	0.331309i	0.754394	−	0.656422i	$-0.227931\pi$
$983$	−5.50449e15	−	9.53406e15i	−0.191282	−	0.331309i	−0.945675	+	0.325113i	$0.894598\pi$
$984$		0			0
$985$	−3.09645e16	+	5.36321e16i	−1.06406	+	1.84300i
$986$		0			0
$987$	−1.07851e15	−	1.03922e15i	−0.0366504	−	0.0353154i
$988$		0			0
$989$	2.48506e16	−	4.30426e16i	0.835137	−	1.44650i
$990$		0			0
$991$	4.82372e15	+	8.35493e15i	0.160316	+	0.277676i	0.934982	−	0.354695i	$-0.115415\pi$
$991$	4.82372e15	+	8.35493e15i	0.160316	+	0.277676i	−0.774666	+	0.632371i	$0.782082\pi$
$992$		0			0
$993$	2.49303e15			0.0819419
$994$		0			0
$995$	−5.98172e16			−1.94446
$996$		0			0
$997$	−5.25892e15	−	9.10872e15i	−0.169073	−	0.292843i	0.769021	−	0.639223i	$-0.220744\pi$
$997$	−5.25892e15	−	9.10872e15i	−0.169073	−	0.292843i	−0.938094	+	0.346381i	$0.887411\pi$
$998$		0			0
$999$	1.55729e15	−	2.69731e15i	0.0495176	−	0.0857670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.12.i.b.37.2	yes	16
3.2	odd	2		252.12.k.d.37.7		16
7.4	even	3	inner	84.12.i.b.25.2	✓	16
21.11	odd	6		252.12.k.d.109.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.12.i.b.25.2	✓	16	7.4	even	3	inner
84.12.i.b.37.2	yes	16	1.1	even	1	trivial
252.12.k.d.37.7		16	3.2	odd	2
252.12.k.d.109.7		16	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-121.500 - 210.444i) q^{3} +(-5539.86 + 9595.32i) q^{5} +(-32020.8 - 30854.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\)	\(q+(-121.500 - 210.444i) q^{3} +(-5539.86 + 9595.32i) q^{5} +(-32020.8 - 30854.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(451860. + 782645. i) q^{11} -761355. q^{13} +2.69237e6 q^{15} +(2.39149e6 + 4.14219e6i) q^{17} +(-2.25438e6 + 3.90470e6i) q^{19} +(-2.60260e6 + 1.04874e7i) q^{21} +(-2.38885e7 + 4.13761e7i) q^{23} +(-3.69661e7 - 6.40271e7i) q^{25} +1.43489e7 q^{27} +1.65205e8 q^{29} +(-2.95464e7 - 5.11759e7i) q^{31} +(1.09802e8 - 1.90183e8i) q^{33} +(4.73449e8 - 1.36321e8i) q^{35} +(1.08530e8 - 1.87980e8i) q^{37} +(9.25047e7 + 1.60223e8i) q^{39} -5.52269e8 q^{41} -1.04028e9 q^{43} +(-3.27123e8 - 5.66594e8i) q^{45} +(-6.93035e7 + 1.20037e8i) q^{47} +(7.33368e7 + 1.97597e9i) q^{49} +(5.81133e8 - 1.00655e9i) q^{51} +(2.34318e9 + 4.05851e9i) q^{53} -1.00130e10 q^{55} +1.09563e9 q^{57} +(-4.49535e9 - 7.78617e9i) q^{59} +(-1.08443e8 + 1.87828e8i) q^{61} +(2.52323e9 - 7.26517e8i) q^{63} +(4.21780e9 - 7.30545e9i) q^{65} +(-8.64085e9 - 1.49664e10i) q^{67} +1.16098e10 q^{69} -5.28267e9 q^{71} +(-5.55061e9 - 9.61394e9i) q^{73} +(-8.98276e9 + 1.55586e10i) q^{75} +(9.67912e9 - 3.90028e10i) q^{77} +(2.14340e9 - 3.71248e9i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -4.61200e10 q^{83} -5.29942e10 q^{85} +(-2.00724e10 - 3.47665e10i) q^{87} +(-8.53894e9 + 1.47899e10i) q^{89} +(2.43792e10 + 2.34912e10i) q^{91} +(-7.17979e9 + 1.24358e10i) q^{93} +(-2.49779e10 - 4.32631e10i) q^{95} +1.57413e11 q^{97} -5.33638e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9	\( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) \) 16 * q - 1944 * q^3 - 2156 * q^5 + 50512 * q^7 - 472392 * q^9 - 222796 * q^11 + 2703176 * q^13 + 1047816 * q^15 + 5114600 * q^17 + 6910556 * q^19 - 18340668 * q^21 - 51387712 * q^23 - 191456372 * q^25 + 229582512 * q^27 + 118854616 * q^29 + 164659160 * q^31 - 54139428 * q^33 + 55239344 * q^35 + 75658364 * q^37 - 328435884 * q^39 - 1815568608 * q^41 + 10754408 * q^43 - 127309644 * q^45 - 1034359464 * q^47 + 4123496848 * q^49 + 1242847800 * q^51 - 665159988 * q^53 - 1264543896 * q^55 - 3358530216 * q^57 + 1040514580 * q^59 - 14391208024 * q^61 + 1474099236 * q^63 - 20938150200 * q^65 - 33307097284 * q^67 + 24974428032 * q^69 + 65848902896 * q^71 + 17709749204 * q^73 - 46523898396 * q^75 + 8594484604 * q^77 - 26626784032 * q^79 - 27894275208 * q^81 - 210306955048 * q^83 - 25867402032 * q^85 - 14440835844 * q^87 - 55951560072 * q^89 + 66078280292 * q^91 + 40012175880 * q^93 + 106810047392 * q^95 - 156216030712 * q^97 + 26311762008 * q^99

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