LMFDB - Embedded newform 72.17.b.b.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,17,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	72.b (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:	$116.873671577$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 20047946100 x^{12} + \cdots + 16\!\cdots\!00 $ x^14 + 20047946100x^12 + 150375970002225333030x^10 + 534365121035003985021711109500x^8 + 929521650393744679697220159577146140625x^6 + 718948651118304969497103032503120835975203125000x^4 + 165555783626963275256526975890091921929357723191406250000x^2 + 166561103584594297516881952271518275269597801038523437500000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.14
Root			$69669.7i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.17.b.b.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(242.759 + 81.2647i) q^{2} +(52328.1 + 39455.5i) q^{4} +557358. i q^{5} -8.55454e6i q^{7} +(9.49679e6 + 1.38306e7i) q^{8} +O(q^{10})$	\(q+(242.759 + 81.2647i) q^{2} +(52328.1 + 39455.5i) q^{4} +557358. i q^{5} -8.55454e6i q^{7} +(9.49679e6 + 1.38306e7i) q^{8} +(-4.52935e7 + 1.35304e8i) q^{10} -1.51024e8 q^{11} -3.64901e8i q^{13} +(6.95181e8 - 2.07669e9i) q^{14} +(1.18149e9 + 4.12926e9i) q^{16} +1.29368e10 q^{17} +2.11348e9 q^{19} +(-2.19908e10 + 2.91655e10i) q^{20} +(-3.66624e10 - 1.22729e10i) q^{22} +7.33433e10i q^{23} -1.58060e11 q^{25} +(2.96535e10 - 8.85830e10i) q^{26} +(3.37523e11 - 4.47643e11i) q^{28} +2.80131e11i q^{29} +9.63483e11i q^{31} +(-4.87445e10 + 1.09843e12i) q^{32} +(3.14054e12 + 1.05131e12i) q^{34} +4.76794e12 q^{35} +5.53641e12i q^{37} +(5.13066e11 + 1.71751e11i) q^{38} +(-7.70860e12 + 5.29311e12i) q^{40} +1.80493e11 q^{41} +2.29216e12 q^{43} +(-7.90278e12 - 5.95871e12i) q^{44} +(-5.96022e12 + 1.78048e13i) q^{46} +1.12569e13i q^{47} -3.99471e13 q^{49} +(-3.83705e13 - 1.28447e13i) q^{50} +(1.43973e13 - 1.90946e13i) q^{52} -8.73423e12i q^{53} -8.41742e13i q^{55} +(1.18314e14 - 8.12407e13i) q^{56} +(-2.27647e13 + 6.80043e13i) q^{58} -2.07936e14 q^{59} -8.30772e12i q^{61} +(-7.82971e13 + 2.33894e14i) q^{62} +(-1.01097e14 + 2.62693e14i) q^{64} +2.03380e14 q^{65} -8.80887e13 q^{67} +(6.76960e14 + 5.10429e14i) q^{68} +(1.15746e15 + 3.87465e14i) q^{70} -6.03023e14i q^{71} -1.18912e15 q^{73} +(-4.49915e14 + 1.34401e15i) q^{74} +(1.10594e14 + 8.33882e13i) q^{76} +1.29194e15i q^{77} -1.98915e15i q^{79} +(-2.30148e15 + 6.58515e14i) q^{80} +(4.38164e13 + 1.46677e13i) q^{82} -1.65008e15 q^{83} +7.21045e15i q^{85} +(5.56443e14 + 1.86272e14i) q^{86} +(-1.43424e15 - 2.08875e15i) q^{88} +2.34380e15 q^{89} -3.12156e15 q^{91} +(-2.89380e15 + 3.83791e15i) q^{92} +(-9.14792e14 + 2.73273e15i) q^{94} +1.17796e15i q^{95} +1.05424e16 q^{97} +(-9.69754e15 - 3.24629e15i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 350 q^{2} - 54220 q^{4} - 10899160 q^{8}+O(q^{10}) $ 14 * q + 350 * q^2 - 54220 * q^4 - 10899160 * q^8	$ 14 q + 350 q^{2} - 54220 q^{4} - 10899160 q^{8} + 87155280 q^{10} + 49140292 q^{11} + 2675193504 q^{14} + 9716374544 q^{16} + 9985136356 q^{17} + 62922133180 q^{19} - 31953450720 q^{20} - 51493048676 q^{22} - 429906632050 q^{25} + 518273679696 q^{26} + 102542376000 q^{28} - 95751080800 q^{32} + 1015818512644 q^{34} + 3057653406720 q^{35} - 9010383442844 q^{38} - 4027933291200 q^{40} - 8719629072668 q^{41} + 16716309178300 q^{43} + 4351929975880 q^{44} + 21043605267744 q^{46} - 104740771400434 q^{49} + 54483696687710 q^{50} - 73249356722400 q^{52} - 110873799752064 q^{56} + 256627273576560 q^{58} - 347007330293180 q^{59} - 346701622780800 q^{62} - 332173589517760 q^{64} - 220877370432000 q^{65} - 614258765968196 q^{67} + 12\!\cdots\!76 q^{68}+ \cdots - 34\!\cdots\!30 q^{98}+O(q^{100}) $ 14 * q + 350 * q^2 - 54220 * q^4 - 10899160 * q^8 + 87155280 * q^10 + 49140292 * q^11 + 2675193504 * q^14 + 9716374544 * q^16 + 9985136356 * q^17 + 62922133180 * q^19 - 31953450720 * q^20 - 51493048676 * q^22 - 429906632050 * q^25 + 518273679696 * q^26 + 102542376000 * q^28 - 95751080800 * q^32 + 1015818512644 * q^34 + 3057653406720 * q^35 - 9010383442844 * q^38 - 4027933291200 * q^40 - 8719629072668 * q^41 + 16716309178300 * q^43 + 4351929975880 * q^44 + 21043605267744 * q^46 - 104740771400434 * q^49 + 54483696687710 * q^50 - 73249356722400 * q^52 - 110873799752064 * q^56 + 256627273576560 * q^58 - 347007330293180 * q^59 - 346701622780800 * q^62 - 332173589517760 * q^64 - 220877370432000 * q^65 - 614258765968196 * q^67 + 1235787871965976 * q^68 - 442172390987520 * q^70 - 542888518370276 * q^73 - 2394643836493776 * q^74 - 614792000883272 * q^76 - 6402194304908160 * q^80 + 4810720063300804 * q^82 - 7362421930746044 * q^83 + 8963192329247716 * q^86 + 3396904358318224 * q^88 + 408131327364580 * q^89 - 7162887702930432 * q^91 + 9213856910218560 * q^92 - 15838781433150144 * q^94 + 18372136634257180 * q^97 - 34005570793293730 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	242.759	+	81.2647i	0.948278	+	0.317440i
$2$	242.759	+	81.2647i	0.948278	+	0.317440i
$3$		0			0
$3$		0			0
$4$	52328.1	+	39455.5i	0.798464	+	0.602043i
$5$			557358.i			1.42684i	0.700739	+	0.713418i	$0.252854\pi$
$5$			557358.i			1.42684i	−0.700739	+	0.713418i	$0.747146\pi$
$6$		0			0
$7$		−	8.55454e6i		−	1.48393i	−0.670441	−	0.741963i	$-0.733895\pi$
$7$		−	8.55454e6i		−	1.48393i	0.670441	−	0.741963i	$-0.266105\pi$
$8$	9.49679e6	+	1.38306e7i	0.566053	+	0.824369i
$9$		0			0
$10$	−4.52935e7	+	1.35304e8i	−0.452935	+	1.35304i
$11$	−1.51024e8			−0.704536			−0.352268	−	0.935899i	$-0.614590\pi$
$11$	−1.51024e8			−0.704536			−0.352268	+	0.935899i	$0.614590\pi$
$12$		0			0
$13$		−	3.64901e8i		−	0.447330i	−0.974666	−	0.223665i	$-0.928198\pi$
$13$		−	3.64901e8i		−	0.447330i	0.974666	−	0.223665i	$-0.0718021\pi$
$14$	6.95181e8	−	2.07669e9i	0.471057	−	1.40717i
$15$		0			0
$16$	1.18149e9	+	4.12926e9i	0.275088	+	0.961419i
$17$	1.29368e10			1.85454			0.927271	−	0.374390i	$-0.122148\pi$
$17$	1.29368e10			1.85454			0.927271	+	0.374390i	$0.122148\pi$
$18$		0			0
$19$	2.11348e9			0.124442			0.0622212	−	0.998062i	$-0.480182\pi$
$19$	2.11348e9			0.124442			0.0622212	+	0.998062i	$0.480182\pi$
$20$	−2.19908e10	+	2.91655e10i	−0.859017	+	1.13928i
$21$		0			0
$22$	−3.66624e10	−	1.22729e10i	−0.668097	−	0.223648i
$23$			7.33433e10i			0.936564i	0.883579	+	0.468282i	$0.155127\pi$
$23$			7.33433e10i			0.936564i	−0.883579	+	0.468282i	$0.844873\pi$
$24$		0			0
$25$	−1.58060e11			−1.03586
$26$	2.96535e10	−	8.85830e10i	0.142000	−	0.424193i
$27$		0			0
$28$	3.37523e11	−	4.47643e11i	0.893387	−	1.18486i
$29$			2.80131e11i			0.559985i	0.960002	+	0.279993i	$0.0903320\pi$
$29$			2.80131e11i			0.559985i	−0.960002	+	0.279993i	$0.909668\pi$
$30$		0			0
$31$			9.63483e11i			1.12967i	0.825205	+	0.564834i	$0.191060\pi$
$31$			9.63483e11i			1.12967i	−0.825205	+	0.564834i	$0.808940\pi$
$32$	−4.87445e10	+	1.09843e12i	−0.0443329	+	0.999017i
$33$		0			0
$34$	3.14054e12	+	1.05131e12i	1.75862	+	0.588706i
$35$	4.76794e12			2.11732
$36$		0			0
$37$			5.53641e12i			1.57621i	0.615540	+	0.788106i	$0.288938\pi$
$37$			5.53641e12i			1.57621i	−0.615540	+	0.788106i	$0.711062\pi$
$38$	5.13066e11	+	1.71751e11i	0.118006	+	0.0395030i
$39$		0			0
$40$	−7.70860e12	+	5.29311e12i	−1.17624	+	0.807665i
$41$	1.80493e11			0.0226042			0.0113021	−	0.999936i	$-0.496402\pi$
$41$	1.80493e11			0.0226042			0.0113021	+	0.999936i	$0.496402\pi$
$42$		0			0
$43$	2.29216e12			0.196109			0.0980544	−	0.995181i	$-0.468738\pi$
$43$	2.29216e12			0.196109			0.0980544	+	0.995181i	$0.468738\pi$
$44$	−7.90278e12	−	5.95871e12i	−0.562547	−	0.424161i
$45$		0			0
$46$	−5.96022e12	+	1.78048e13i	−0.297303	+	0.888124i
$47$			1.12569e13i			0.472757i	0.971661	+	0.236378i	$0.0759604\pi$
$47$			1.12569e13i			0.472757i	−0.971661	+	0.236378i	$0.924040\pi$
$48$		0			0
$49$	−3.99471e13			−1.20204
$50$	−3.83705e13	−	1.28447e13i	−0.982286	−	0.328824i
$51$		0			0
$52$	1.43973e13	−	1.90946e13i	0.269312	−	0.357177i
$53$		−	8.73423e12i		−	0.140287i	−0.997537	−	0.0701435i	$-0.977654\pi$
$53$		−	8.73423e12i		−	0.140287i	0.997537	−	0.0701435i	$-0.0223457\pi$
$54$		0			0
$55$		−	8.41742e13i		−	1.00526i
$56$	1.18314e14	−	8.12407e13i	1.22330	−	0.839981i
$57$		0			0
$58$	−2.27647e13	+	6.80043e13i	−0.177762	+	0.531022i
$59$	−2.07936e14			−1.41616			−0.708082	−	0.706131i	$-0.750439\pi$
$59$	−2.07936e14			−1.41616			−0.708082	+	0.706131i	$0.750439\pi$
$60$		0			0
$61$		−	8.30772e12i		−	0.0433354i	−0.999765	−	0.0216677i	$-0.993102\pi$
$61$		−	8.30772e12i		−	0.0433354i	0.999765	−	0.0216677i	$-0.00689759\pi$
$62$	−7.82971e13	+	2.33894e14i	−0.358602	+	1.07124i
$63$		0			0
$64$	−1.01097e14	+	2.62693e14i	−0.359168	+	0.933273i
$65$	2.03380e14			0.638267
$66$		0			0
$67$	−8.80887e13			−0.216931			−0.108466	−	0.994100i	$-0.534594\pi$
$67$	−8.80887e13			−0.216931			−0.108466	+	0.994100i	$0.534594\pi$
$68$	6.76960e14	+	5.10429e14i	1.48078	+	1.11651i
$69$		0			0
$70$	1.15746e15	+	3.87465e14i	2.00781	+	0.672122i
$71$		−	6.03023e14i		−	0.933829i	−0.884302	−	0.466915i	$-0.845366\pi$
$71$		−	6.03023e14i		−	0.933829i	0.884302	−	0.466915i	$-0.154634\pi$
$72$		0			0
$73$	−1.18912e15			−1.47449			−0.737244	−	0.675627i	$-0.763873\pi$
$73$	−1.18912e15			−1.47449			−0.737244	+	0.675627i	$0.763873\pi$
$74$	−4.49915e14	+	1.34401e15i	−0.500353	+	1.49469i
$75$		0			0
$76$	1.10594e14	+	8.33882e13i	0.0993627	+	0.0749197i
$77$			1.29194e15i			1.04548i
$78$		0			0
$79$		−	1.98915e15i		−	1.31115i	−0.755132	−	0.655573i	$-0.772427\pi$
$79$		−	1.98915e15i		−	1.31115i	0.755132	−	0.655573i	$-0.227573\pi$
$80$	−2.30148e15	+	6.58515e14i	−1.37179	+	0.392506i
$81$		0			0
$82$	4.38164e13	+	1.46677e13i	0.0214351	+	0.00717549i
$83$	−1.65008e15			−0.732621			−0.366311	−	0.930493i	$-0.619379\pi$
$83$	−1.65008e15			−0.732621			−0.366311	+	0.930493i	$0.619379\pi$
$84$		0			0
$85$			7.21045e15i			2.64613i
$86$	5.56443e14	+	1.86272e14i	0.185966	+	0.0622528i
$87$		0			0
$88$	−1.43424e15	−	2.08875e15i	−0.398805	−	0.580798i
$89$	2.34380e15			0.595389			0.297695	−	0.954661i	$-0.403782\pi$
$89$	2.34380e15			0.595389			0.297695	+	0.954661i	$0.403782\pi$
$90$		0			0
$91$	−3.12156e15			−0.663804
$92$	−2.89380e15	+	3.83791e15i	−0.563852	+	0.747812i
$93$		0			0
$94$	−9.14792e14	+	2.73273e15i	−0.150072	+	0.448305i
$95$			1.17796e15i			0.177559i
$96$		0			0
$97$	1.05424e16			1.34513			0.672566	−	0.740038i	$-0.265192\pi$
$97$	1.05424e16			1.34513			0.672566	+	0.740038i	$0.265192\pi$
$98$	−9.69754e15	−	3.24629e15i	−1.13986	−	0.381574i
$99$		0			0
$100$	−8.27098e15	−	6.23634e15i	−0.827098	−	0.623634i
$101$			1.99013e16i			1.83785i	0.394431	+	0.918926i	$0.370942\pi$
$101$			1.99013e16i			1.83785i	−0.394431	+	0.918926i	$0.629058\pi$
$102$		0			0
$103$			6.97952e15i			0.550970i	0.961305	+	0.275485i	$0.0888384\pi$
$103$			6.97952e15i			0.550970i	−0.961305	+	0.275485i	$0.911162\pi$
$104$	5.04680e15	−	3.46539e15i	0.368765	−	0.253212i
$105$		0			0
$106$	7.09784e14	−	2.12031e15i	0.0445327	−	0.133031i
$107$	1.15042e16			0.669555			0.334777	−	0.942297i	$-0.391339\pi$
$107$	1.15042e16			0.669555			0.334777	+	0.942297i	$0.391339\pi$
$108$		0			0
$109$			2.34185e16i			1.17530i	0.809116	+	0.587648i	$0.199946\pi$
$109$			2.34185e16i			1.17530i	−0.809116	+	0.587648i	$0.800054\pi$
$110$	6.84039e15	−	2.04341e16i	0.319109	−	0.953265i
$111$		0			0
$112$	3.53239e16	−	1.01071e16i	1.42667	−	0.408210i
$113$	1.76133e16			0.662542			0.331271	−	0.943536i	$-0.392523\pi$
$113$	1.76133e16			0.662542			0.331271	+	0.943536i	$0.392523\pi$
$114$		0			0
$115$	−4.08785e16			−1.33632
$116$	−1.10527e16	+	1.46587e16i	−0.337135	+	0.447128i
$117$		0			0
$118$	−5.04784e16	−	1.68978e16i	−1.34292	−	0.449547i
$119$		−	1.10669e17i		−	2.75200i
$120$		0			0
$121$	−2.31416e16			−0.503628
$122$	6.75124e14	−	2.01678e15i	0.0137564	−	0.0410940i
$123$		0			0
$124$	−3.80147e16	+	5.04173e16i	−0.680108	+	0.901998i
$125$		−	3.04994e15i		−	0.0511695i
$126$		0			0
$127$			1.43339e15i			0.0211805i	0.999944	+	0.0105902i	$0.00337104\pi$
$127$			1.43339e15i			0.0211805i	−0.999944	+	0.0105902i	$0.996629\pi$
$128$	−4.58898e16	+	5.55556e16i	−0.636849	+	0.770988i
$129$		0			0
$130$	4.93725e16	+	1.65276e16i	0.605254	+	0.202611i
$131$	3.24094e16			0.373681			0.186840	−	0.982390i	$-0.440175\pi$
$131$	3.24094e16			0.373681			0.186840	+	0.982390i	$0.440175\pi$
$132$		0			0
$133$		−	1.80798e16i		−	0.184663i
$134$	−2.13843e16	−	7.15850e15i	−0.205711	−	0.0688626i
$135$		0			0
$136$	1.22859e17	+	1.78924e17i	1.04977	+	1.52883i
$137$	−1.75284e17			−1.41246			−0.706231	−	0.707982i	$-0.749606\pi$
$137$	−1.75284e17			−1.41246			−0.706231	+	0.707982i	$0.749606\pi$
$138$		0			0
$139$	−6.24449e16			−0.448104			−0.224052	−	0.974577i	$-0.571928\pi$
$139$	−6.24449e16			−0.448104			−0.224052	+	0.974577i	$0.571928\pi$
$140$	2.49497e17	+	1.88121e17i	1.69060	+	1.27472i
$141$		0			0
$142$	4.90045e16	−	1.46390e17i	0.296435	−	0.885530i
$143$			5.51086e16i			0.315160i
$144$		0			0
$145$	−1.56133e17			−0.799008
$146$	−2.88669e17	−	9.66330e16i	−1.39822	−	0.468061i
$147$		0			0
$148$	−2.18442e17	+	2.89710e17i	−0.948947	+	1.25855i
$149$			1.99108e17i			0.819593i	0.912177	+	0.409796i	$0.134400\pi$
$149$			1.99108e17i			0.819593i	−0.912177	+	0.409796i	$0.865600\pi$
$150$		0			0
$151$			9.45575e16i			0.349849i	0.984582	+	0.174924i	$0.0559681\pi$
$151$			9.45575e16i			0.349849i	−0.984582	+	0.174924i	$0.944032\pi$
$152$	2.00712e16	+	2.92307e16i	0.0704410	+	0.102586i
$153$		0			0
$154$	−1.04989e17	+	3.13630e17i	−0.331877	+	0.991406i
$155$	−5.37005e17			−1.61185
$156$		0			0
$157$			7.05881e16i			0.191220i	0.995419	+	0.0956102i	$0.0304802\pi$
$157$			7.05881e16i			0.191220i	−0.995419	+	0.0956102i	$0.969520\pi$
$158$	1.61648e17	−	4.82885e17i	0.416211	−	1.24333i
$159$		0			0
$160$	−6.12219e17	−	2.71681e16i	−1.42543	−	0.0632558i
$161$	6.27418e17			1.38979
$162$		0			0
$163$	2.34479e17			0.470547			0.235274	−	0.971929i	$-0.424401\pi$
$163$	2.34479e17			0.470547			0.235274	+	0.971929i	$0.424401\pi$
$164$	9.44486e15	+	7.12144e15i	0.0180487	+	0.0136087i
$165$		0			0
$166$	−4.00571e17	−	1.34093e17i	−0.694729	−	0.232563i
$167$			9.91844e17i			1.63950i	0.572721	+	0.819751i	$0.305888\pi$
$167$			9.91844e17i			1.63950i	−0.572721	+	0.819751i	$0.694112\pi$
$168$		0			0
$169$	5.32264e17			0.799896
$170$	−5.85955e17	+	1.75040e18i	−0.839987	+	2.50927i
$171$		0			0
$172$	1.19944e17	+	9.04383e16i	0.156586	+	0.118066i
$173$			4.60112e17i			0.573449i	0.958013	+	0.286724i	$0.0925664\pi$
$173$			4.60112e17i			0.573449i	−0.958013	+	0.286724i	$0.907434\pi$
$174$		0			0
$175$			1.35213e18i			1.53714i
$176$	−1.78434e17	−	6.23616e17i	−0.193810	−	0.677355i
$177$		0			0
$178$	5.68980e17	+	1.90468e17i	0.564595	+	0.189000i
$179$	1.47277e18			1.39737			0.698683	−	0.715431i	$-0.253770\pi$
$179$	1.47277e18			1.39737			0.698683	+	0.715431i	$0.253770\pi$
$180$		0			0
$181$			6.60815e17i			0.573655i	0.957982	+	0.286828i	$0.0926007\pi$
$181$			6.60815e17i			0.573655i	−0.957982	+	0.286828i	$0.907399\pi$
$182$	−7.57787e17	−	2.53672e17i	−0.629471	−	0.210718i
$183$		0			0
$184$	−1.01438e18	+	6.96526e17i	−0.772074	+	0.530145i
$185$	−3.08576e18			−2.24900
$186$		0			0
$187$	−1.95377e18			−1.30659
$188$	−4.44148e17	+	5.89054e17i	−0.284620	+	0.377479i
$189$		0			0
$190$	−9.57267e16	+	2.85961e17i	−0.0563643	+	0.168375i
$191$		−	1.53435e18i		−	0.866280i	−0.901327	−	0.433140i	$-0.857406\pi$
$191$		−	1.53435e18i		−	0.866280i	0.901327	−	0.433140i	$-0.142594\pi$
$192$		0			0
$193$	7.58207e16			0.0393849			0.0196924	−	0.999806i	$-0.493731\pi$
$193$	7.58207e16			0.0393849			0.0196924	+	0.999806i	$0.493731\pi$
$194$	2.55926e18	+	8.56723e17i	1.27556	+	0.426999i
$195$		0			0
$196$	−2.09036e18	−	1.57613e18i	−0.959781	−	0.723677i
$197$		−	9.73556e17i		−	0.429172i	−0.976705	−	0.214586i	$-0.931160\pi$
$197$		−	9.73556e17i		−	0.429172i	0.976705	−	0.214586i	$-0.0688402\pi$
$198$		0			0
$199$		−	8.87051e17i		−	0.360681i	−0.983604	−	0.180341i	$-0.942280\pi$
$199$		−	8.87051e17i		−	0.360681i	0.983604	−	0.180341i	$-0.0577200\pi$
$200$	−1.50106e18	−	2.18607e18i	−0.586353	−	0.853932i
$201$		0			0
$202$	−1.61727e18	+	4.83122e18i	−0.583408	+	1.74279i
$203$	2.39639e18			0.830977
$204$		0			0
$205$			1.00599e17i			0.0322525i
$206$	−5.67188e17	+	1.69434e18i	−0.174900	+	0.522473i
$207$		0			0
$208$	1.50677e18	−	4.31128e17i	0.430072	−	0.123055i
$209$	−3.19185e17			−0.0876742
$210$		0			0
$211$	1.81860e17			0.0462890			0.0231445	−	0.999732i	$-0.492632\pi$
$211$	1.81860e17			0.0462890			0.0231445	+	0.999732i	$0.492632\pi$
$212$	3.44613e17	−	4.57046e17i	0.0844588	−	0.112014i
$213$		0			0
$214$	2.79275e18	+	9.34885e17i	0.634924	+	0.212544i
$215$			1.27755e18i			0.279815i
$216$		0			0
$217$	8.24215e18			1.67634
$218$	−1.90310e18	+	5.68506e18i	−0.373086	+	1.11451i
$219$		0			0
$220$	3.32114e18	−	4.40468e18i	0.605209	−	0.802662i
$221$		−	4.72066e18i		−	0.829592i
$222$		0			0
$223$		−	4.73123e18i		−	0.773633i	−0.922157	−	0.386816i	$-0.873575\pi$
$223$		−	4.73123e18i		−	0.773633i	0.922157	−	0.386816i	$-0.126425\pi$
$224$	9.39656e18	+	4.16987e17i	1.48247	+	0.0657867i
$225$		0			0
$226$	4.27579e18	+	1.43134e18i	0.628274	+	0.210317i
$227$	1.01230e19			1.43583			0.717913	−	0.696133i	$-0.245098\pi$
$227$	1.01230e19			1.43583			0.717913	+	0.696133i	$0.245098\pi$
$228$		0			0
$229$		−	1.24157e19i		−	1.64168i	−0.571159	−	0.820840i	$-0.693506\pi$
$229$		−	1.24157e19i		−	1.64168i	0.571159	−	0.820840i	$-0.306494\pi$
$230$	−9.92362e18	−	3.32197e18i	−1.26721	−	0.424203i
$231$		0			0
$232$	−3.87438e18	+	2.66034e18i	−0.461634	+	0.316981i
$233$	9.63007e18			1.10862			0.554309	−	0.832311i	$-0.312982\pi$
$233$	9.63007e18			1.10862			0.554309	+	0.832311i	$0.312982\pi$
$234$		0			0
$235$	−6.27415e18			−0.674546
$236$	−1.08809e19	−	8.20421e18i	−1.13075	−	0.852591i
$237$		0			0
$238$	8.99345e18	−	2.68658e19i	0.873596	−	2.60967i
$239$		−	1.17222e19i		−	1.10109i	−0.834804	−	0.550547i	$-0.814419\pi$
$239$		−	1.17222e19i		−	1.10109i	0.834804	−	0.550547i	$-0.185581\pi$
$240$		0			0
$241$	−8.99136e18			−0.790112			−0.395056	−	0.918657i	$-0.629275\pi$
$241$	−8.99136e18			−0.790112			−0.395056	+	0.918657i	$0.629275\pi$
$242$	−5.61783e18	−	1.88059e18i	−0.477580	−	0.159872i
$243$		0			0
$244$	3.27785e17	−	4.34727e17i	0.0260898	−	0.0346018i
$245$		−	2.22649e19i		−	1.71511i
$246$		0			0
$247$		−	7.71209e17i		−	0.0556668i
$248$	−1.33256e19	+	9.15000e18i	−0.931263	+	0.639452i
$249$		0			0
$250$	2.47852e17	−	7.40401e17i	0.0162432	−	0.0485229i
$251$	8.44272e17			0.0535911			0.0267955	−	0.999641i	$-0.491470\pi$
$251$	8.44272e17			0.0535911			0.0267955	+	0.999641i	$0.491470\pi$
$252$		0			0
$253$		−	1.10766e19i		−	0.659844i
$254$	−1.16484e17	+	3.47969e17i	−0.00672353	+	0.0200850i
$255$		0			0
$256$	−1.56549e19	+	9.75740e18i	−0.848653	+	0.528950i
$257$	1.12539e19			0.591343			0.295672	−	0.955290i	$-0.404457\pi$
$257$	1.12539e19			0.591343			0.295672	+	0.955290i	$0.404457\pi$
$258$		0			0
$259$	4.73614e19			2.33898
$260$	1.06425e19	+	8.02447e18i	0.509633	+	0.384264i
$261$		0			0
$262$	7.86768e18	+	2.63374e18i	0.354353	+	0.118621i
$263$		−	2.11514e19i		−	0.924046i	−0.886868	−	0.462023i	$-0.847124\pi$
$263$		−	2.11514e19i		−	0.924046i	0.886868	−	0.462023i	$-0.152876\pi$
$264$		0			0
$265$	4.86809e18			0.200167
$266$	1.46925e18	−	4.38904e18i	0.0586195	−	0.175112i
$267$		0			0
$268$	−4.60951e18	−	3.47558e18i	−0.173212	−	0.130602i
$269$			3.46645e19i			1.26435i	0.774826	+	0.632174i	$0.217837\pi$
$269$			3.46645e19i			1.26435i	−0.774826	+	0.632174i	$0.782163\pi$
$270$		0			0
$271$			1.79486e19i			0.616986i	0.951227	+	0.308493i	$0.0998246\pi$
$271$			1.79486e19i			0.616986i	−0.951227	+	0.308493i	$0.900175\pi$
$272$	1.52848e19	+	5.34196e19i	0.510163	+	1.78299i
$273$		0			0
$274$	−4.25517e19	−	1.42444e19i	−1.33941	−	0.448372i
$275$	2.38708e19			0.729803
$276$		0			0
$277$			1.89220e19i			0.545920i	0.962025	+	0.272960i	$0.0880027\pi$
$277$			1.89220e19i			0.545920i	−0.962025	+	0.272960i	$0.911997\pi$
$278$	−1.51591e19	−	5.07456e18i	−0.424927	−	0.142246i
$279$		0			0
$280$	4.52801e19	+	6.59435e19i	1.19851	+	1.74545i
$281$	2.99742e19			0.771077			0.385538	−	0.922692i	$-0.374016\pi$
$281$	2.99742e19			0.771077			0.385538	+	0.922692i	$0.374016\pi$
$282$		0			0
$283$	−2.97748e19			−0.723697			−0.361849	−	0.932237i	$-0.617854\pi$
$283$	−2.97748e19			−0.723697			−0.361849	+	0.932237i	$0.617854\pi$
$284$	2.37926e19	−	3.15551e19i	0.562205	−	0.745629i
$285$		0			0
$286$	−4.47839e18	+	1.33781e19i	−0.100045	+	0.298860i
$287$		−	1.54403e18i		−	0.0335430i
$288$		0			0
$289$	1.18701e20			2.43933
$290$	−3.79027e19	−	1.26881e19i	−0.757681	−	0.253637i
$291$		0			0
$292$	−6.22241e19	−	4.69171e19i	−1.17732	−	0.887705i
$293$		−	3.21807e18i		−	0.0592453i	−0.999561	−	0.0296227i	$-0.990569\pi$
$293$		−	3.21807e18i		−	0.0592453i	0.999561	−	0.0296227i	$-0.00943057\pi$
$294$		0			0
$295$		−	1.15895e20i		−	2.02063i
$296$	−7.65720e19	+	5.25782e19i	−1.29938	+	0.892219i
$297$		0			0
$298$	−1.61804e19	+	4.83353e19i	−0.260172	+	0.777202i
$299$	2.67630e19			0.418953
$300$		0			0
$301$		−	1.96084e19i		−	0.291011i
$302$	−7.68418e18	+	2.29547e19i	−0.111056	+	0.331754i
$303$		0			0
$304$	2.49706e18	+	8.72710e18i	0.0342326	+	0.119641i
$305$	4.63037e18			0.0618326
$306$		0			0
$307$	5.81978e19			0.737564			0.368782	−	0.929516i	$-0.379775\pi$
$307$	5.81978e19			0.737564			0.368782	+	0.929516i	$0.379775\pi$
$308$	−5.09740e19	+	6.76046e19i	−0.629424	+	0.834777i
$309$		0			0
$310$	−1.30363e20	−	4.36395e19i	−1.52848	−	0.511666i
$311$		−	1.04256e20i		−	1.19129i	−0.803248	−	0.595645i	$-0.796896\pi$
$311$		−	1.04256e20i		−	1.19129i	0.803248	−	0.595645i	$-0.203104\pi$
$312$		0			0
$313$	−1.60356e20			−1.74073			−0.870365	−	0.492407i	$-0.836117\pi$
$313$	−1.60356e20			−1.74073			−0.870365	+	0.492407i	$0.836117\pi$
$314$	−5.73632e18	+	1.71359e19i	−0.0607010	+	0.181330i
$315$		0			0
$316$	7.84830e19	−	1.04089e20i	0.789367	−	1.04690i
$317$		−	1.13662e19i		−	0.111466i	−0.998446	−	0.0557329i	$-0.982250\pi$
$317$		−	1.13662e19i		−	0.111466i	0.998446	−	0.0557329i	$-0.0177495\pi$
$318$		0			0
$319$		−	4.23064e19i		−	0.394530i
$320$	−1.46414e20	−	5.63471e19i	−1.33163	−	0.512474i
$321$		0			0
$322$	1.52311e20	+	5.09869e19i	1.31791	+	0.441176i
$323$	2.73417e19			0.230784
$324$		0			0
$325$			5.76762e19i			0.463372i
$326$	5.69220e19	+	1.90549e19i	0.446210	+	0.149371i
$327$		0			0
$328$	1.71411e18	+	2.49633e18i	0.0127952	+	0.0186342i
$329$	9.62979e19			0.701535
$330$		0			0
$331$	4.34350e18			0.0301450			0.0150725	−	0.999886i	$-0.495202\pi$
$331$	4.34350e18			0.0301450			0.0150725	+	0.999886i	$0.495202\pi$
$332$	−8.63454e19	−	6.51046e19i	−0.584971	−	0.441070i
$333$		0			0
$334$	−8.06019e19	+	2.40779e20i	−0.520443	+	1.55470i
$335$		−	4.90969e19i		−	0.309525i
$336$		0			0
$337$	5.38785e19			0.323874			0.161937	−	0.986801i	$-0.448226\pi$
$337$	5.38785e19			0.323874			0.161937	+	0.986801i	$0.448226\pi$
$338$	1.29212e20	+	4.32543e19i	0.758524	+	0.253919i
$339$		0			0
$340$	−2.84492e20	+	3.77309e20i	−1.59308	+	2.11284i
$341$		−	1.45509e20i		−	0.795892i
$342$		0			0
$343$			5.74370e19i			0.299805i
$344$	2.17682e19	+	3.17020e19i	0.111008	+	0.161666i
$345$		0			0
$346$	−3.73908e19	+	1.11696e20i	−0.182036	+	0.543789i
$347$	−1.01011e18			−0.00480544			−0.00240272	−	0.999997i	$-0.500765\pi$
$347$	−1.01011e18			−0.00480544			−0.00240272	+	0.999997i	$0.500765\pi$
$348$		0			0
$349$		−	1.68723e20i		−	0.766602i	−0.923624	−	0.383301i	$-0.874787\pi$
$349$		−	1.68723e20i		−	0.766602i	0.923624	−	0.383301i	$-0.125213\pi$
$350$	−1.09880e20	+	3.28242e20i	−0.487951	+	1.45764i
$351$		0			0
$352$	7.36157e18	−	1.65889e20i	0.0312341	−	0.703844i
$353$	2.84133e20			1.17849			0.589243	−	0.807956i	$-0.299426\pi$
$353$	2.84133e20			1.17849			0.589243	+	0.807956i	$0.299426\pi$
$354$		0			0
$355$	3.36100e20			1.33242
$356$	1.22647e20	+	9.24759e19i	0.475397	+	0.358450i
$357$		0			0
$358$	3.57528e20	+	1.19684e20i	1.32509	+	0.443580i
$359$			2.04614e20i			0.741617i	0.928709	+	0.370809i	$0.120919\pi$
$359$			2.04614e20i			0.741617i	−0.928709	+	0.370809i	$0.879081\pi$
$360$		0			0
$361$	−2.83975e20			−0.984514
$362$	−5.37009e19	+	1.60419e20i	−0.182101	+	0.543985i
$363$		0			0
$364$	−1.63345e20	−	1.23163e20i	−0.530024	−	0.399639i
$365$		−	6.62763e20i		−	2.10385i
$366$		0			0
$367$			1.00923e20i			0.306664i	0.988175	+	0.153332i	$0.0490004\pi$
$367$			1.00923e20i			0.306664i	−0.988175	+	0.153332i	$0.951000\pi$
$368$	−3.02854e20	+	8.66547e19i	−0.900431	+	0.257638i
$369$		0			0
$370$	−7.49097e20	−	2.50763e20i	−2.13267	−	0.713922i
$371$	−7.47173e19			−0.208176
$372$		0			0
$373$			6.48351e20i			1.73037i	0.501451	+	0.865186i	$0.332800\pi$
$373$			6.48351e20i			1.73037i	−0.501451	+	0.865186i	$0.667200\pi$
$374$	−4.74295e20	−	1.58772e20i	−1.23901	−	0.414765i
$375$		0			0
$376$	−1.55690e20	+	1.06905e20i	−0.389726	+	0.267605i
$377$	1.02220e20			0.250498
$378$		0			0
$379$	4.49795e18			0.0105658			0.00528288	−	0.999986i	$-0.498318\pi$
$379$	4.49795e18			0.0105658			0.00528288	+	0.999986i	$0.498318\pi$
$380$	−4.64771e19	+	6.16405e19i	−0.106898	+	0.141774i
$381$		0			0
$382$	1.24689e20	−	3.72478e20i	0.274992	−	0.821474i
$383$			5.53477e20i			1.19539i	0.801724	+	0.597694i	$0.203916\pi$
$383$			5.53477e20i			1.19539i	−0.801724	+	0.597694i	$0.796084\pi$
$384$		0			0
$385$	−7.20072e20			−1.49173
$386$	1.84062e19	+	6.16155e18i	0.0373478	+	0.0125023i
$387$		0			0
$388$	5.51663e20	+	4.15955e20i	1.07404	+	0.809827i
$389$			1.51215e19i			0.0288402i	0.999896	+	0.0144201i	$0.00459022\pi$
$389$			1.51215e19i			0.0288402i	−0.999896	+	0.0144201i	$0.995410\pi$
$390$		0			0
$391$			9.48830e20i			1.73690i
$392$	−3.79370e20	−	5.52494e20i	−0.680416	−	0.990920i
$393$		0			0
$394$	7.91157e19	−	2.36340e20i	0.136236	−	0.406974i
$395$	1.10867e21			1.87079
$396$		0			0
$397$		−	6.46671e20i		−	1.04800i	−0.851720	−	0.523998i	$-0.824440\pi$
$397$		−	6.46671e20i		−	1.04800i	0.851720	−	0.523998i	$-0.175560\pi$
$398$	7.20859e19	−	2.15340e20i	0.114495	−	0.342026i
$399$		0			0
$400$	−1.86747e20	−	6.52671e20i	−0.284953	−	0.995898i
$401$	−2.36360e20			−0.353524			−0.176762	−	0.984254i	$-0.556562\pi$
$401$	−2.36360e20			−0.353524			−0.176762	+	0.984254i	$0.556562\pi$
$402$		0			0
$403$	3.51576e20			0.505334
$404$	−7.85216e20	+	1.04140e21i	−1.10647	+	1.46746i
$405$		0			0
$406$	5.81745e20	+	1.94742e20i	0.787997	+	0.263785i
$407$		−	8.36129e20i		−	1.11050i
$408$		0			0
$409$	1.09893e21			1.40341			0.701706	−	0.712467i	$-0.252422\pi$
$409$	1.09893e21			1.40341			0.701706	+	0.712467i	$0.252422\pi$
$410$	−8.17517e18	+	2.44214e19i	−0.0102382	+	0.0305844i
$411$		0			0
$412$	−2.75380e20	+	3.65225e20i	−0.331708	+	0.439929i
$413$			1.77879e21i			2.10148i
$414$		0			0
$415$		−	9.19684e20i		−	1.04533i
$416$	4.00818e20	+	1.77869e19i	0.446890	+	0.0198314i
$417$		0			0
$418$	−7.74851e19	−	2.59384e19i	−0.0831395	−	0.0278313i
$419$	5.87615e19			0.0618559			0.0309279	−	0.999522i	$-0.490154\pi$
$419$	5.87615e19			0.0618559			0.0309279	+	0.999522i	$0.490154\pi$
$420$		0			0
$421$		−	8.68806e20i		−	0.880372i	−0.897907	−	0.440186i	$-0.854913\pi$
$421$		−	8.68806e20i		−	0.880372i	0.897907	−	0.440186i	$-0.145087\pi$
$422$	4.41483e19	+	1.47788e19i	0.0438949	+	0.0146940i
$423$		0			0
$424$	1.20800e20	−	8.29472e19i	0.115648	−	0.0794099i
$425$	−2.04480e21			−1.92105
$426$		0			0
$427$	−7.10687e19			−0.0643065
$428$	6.01993e20	+	4.53904e20i	0.534615	+	0.403101i
$429$		0			0
$430$	−1.03820e20	+	3.10138e20i	−0.0888246	+	0.265343i
$431$		−	1.92605e20i		−	0.161752i	−0.996724	−	0.0808758i	$-0.974228\pi$
$431$		−	1.92605e20i		−	0.161752i	0.996724	−	0.0808758i	$-0.0257717\pi$
$432$		0			0
$433$	−2.34786e20			−0.190006			−0.0950032	−	0.995477i	$-0.530286\pi$
$433$	−2.34786e20			−0.190006			−0.0950032	+	0.995477i	$0.530286\pi$
$434$	2.00086e21	+	6.69796e20i	1.58964	+	0.532138i
$435$		0			0
$436$	−9.23990e20	+	1.22545e21i	−0.707579	+	0.938432i
$437$			1.55009e20i			0.116548i
$438$		0			0
$439$		−	2.18515e21i		−	1.58404i	−0.610497	−	0.792018i	$-0.709030\pi$
$439$		−	2.18515e21i		−	1.58404i	0.610497	−	0.792018i	$-0.290970\pi$
$440$	1.16418e21	−	7.99385e20i	0.828704	−	0.569030i
$441$		0			0
$442$	3.83623e20	−	1.14598e21i	0.263346	−	0.786685i
$443$	−1.07184e21			−0.722602			−0.361301	−	0.932449i	$-0.617667\pi$
$443$	−1.07184e21			−0.722602			−0.361301	+	0.932449i	$0.617667\pi$
$444$		0			0
$445$			1.30634e21i			0.849523i
$446$	3.84481e20	−	1.14855e21i	0.245582	−	0.733619i
$447$		0			0
$448$	2.24722e21	+	8.64836e20i	1.38491	+	0.532978i
$449$	1.09657e21			0.663842			0.331921	−	0.943307i	$-0.392303\pi$
$449$	1.09657e21			0.663842			0.331921	+	0.943307i	$0.392303\pi$
$450$		0			0
$451$	−2.72587e19			−0.0159255
$452$	9.21671e20	+	6.94942e20i	0.529016	+	0.398879i
$453$		0			0
$454$	2.45745e21	+	8.22641e20i	1.36156	+	0.455789i
$455$		−	1.73982e21i		−	0.947140i
$456$		0			0
$457$	−6.92574e20			−0.364030			−0.182015	−	0.983296i	$-0.558262\pi$
$457$	−6.92574e20			−0.364030			−0.182015	+	0.983296i	$0.558262\pi$
$458$	1.00896e21	−	3.01403e21i	0.521135	−	1.55677i
$459$		0			0
$460$	−2.13909e21	−	1.61288e21i	−1.06701	−	0.804525i
$461$		−	1.76325e21i		−	0.864384i	−0.901782	−	0.432192i	$-0.857740\pi$
$461$		−	1.76325e21i		−	0.864384i	0.901782	−	0.432192i	$-0.142260\pi$
$462$		0			0
$463$		−	8.88321e20i		−	0.420651i	−0.977631	−	0.210325i	$-0.932548\pi$
$463$		−	8.88321e20i		−	0.420651i	0.977631	−	0.210325i	$-0.0674524\pi$
$464$	−1.15673e21	+	3.30973e20i	−0.538381	+	0.154045i
$465$		0			0
$466$	2.33779e21	+	7.82585e20i	1.05128	+	0.351920i
$467$	−2.42168e21			−1.07049			−0.535244	−	0.844697i	$-0.679780\pi$
$467$	−2.42168e21			−1.07049			−0.535244	+	0.844697i	$0.679780\pi$
$468$		0			0
$469$			7.53558e20i			0.321910i
$470$	−1.52311e21	−	5.09866e20i	−0.639658	−	0.214128i
$471$		0			0
$472$	−1.97472e21	−	2.87588e21i	−0.801624	−	1.16744i
$473$	−3.46170e20			−0.138166
$474$		0			0
$475$	−3.34056e20			−0.128905
$476$	4.36649e21	−	5.79108e21i	1.65682	−	2.19737i
$477$		0			0
$478$	9.52597e20	−	2.84566e21i	0.349531	−	1.04414i
$479$		−	2.90885e21i		−	1.04963i	−0.851215	−	0.524817i	$-0.824134\pi$
$479$		−	2.90885e21i		−	1.04963i	0.851215	−	0.524817i	$-0.175866\pi$
$480$		0			0
$481$	2.02024e21			0.705087
$482$	−2.18274e21	−	7.30680e20i	−0.749247	−	0.250813i
$483$		0			0
$484$	−1.21096e21	−	9.13063e20i	−0.402129	−	0.303206i
$485$			5.87588e21i			1.91928i
$486$		0			0
$487$		−	3.94387e21i		−	1.24650i	−0.782024	−	0.623249i	$-0.785813\pi$
$487$		−	3.94387e21i		−	1.24650i	0.782024	−	0.623249i	$-0.214187\pi$
$488$	1.14901e20	−	7.88967e19i	0.0357244	−	0.0245301i
$489$		0			0
$490$	1.80935e21	−	5.40500e21i	0.544444	−	1.62640i
$491$	6.54682e21			1.93811			0.969056	−	0.246842i	$-0.0793929\pi$
$491$	6.54682e21			1.93811			0.969056	+	0.246842i	$0.0793929\pi$
$492$		0			0
$493$			3.62401e21i			1.03852i
$494$	6.26720e19	−	1.87218e20i	0.0176709	−	0.0527876i
$495$		0			0
$496$	−3.97848e21	+	1.13835e21i	−1.08608	+	0.310758i
$497$	−5.15859e21			−1.38573
$498$		0			0
$499$	5.84564e21			1.52064			0.760322	−	0.649546i	$-0.225041\pi$
$499$	5.84564e21			1.52064			0.760322	+	0.649546i	$0.225041\pi$
$500$	1.20337e20	−	1.59598e20i	0.0308062	−	0.0408570i
$501$		0			0
$502$	2.04955e20	+	6.86095e19i	0.0508192	+	0.0170120i
$503$			5.16336e21i			1.26005i	0.776574	+	0.630026i	$0.216956\pi$
$503$			5.16336e21i			1.26005i	−0.776574	+	0.630026i	$0.783044\pi$
$504$		0			0
$505$	−1.10921e22			−2.62231
$506$	9.00134e20	−	2.68894e21i	0.209461	−	0.625715i
$507$		0			0
$508$	−5.65552e19	+	7.50067e19i	−0.0127516	+	0.0169118i
$509$			1.25680e21i			0.278948i	0.990226	+	0.139474i	$0.0445412\pi$
$509$			1.25680e21i			0.278948i	−0.990226	+	0.139474i	$0.955459\pi$
$510$		0			0
$511$			1.01723e22i			2.18803i
$512$	−4.59330e21	+	1.09651e21i	−0.972669	+	0.232195i
$513$		0			0
$514$	2.73200e21	+	9.14548e20i	0.560758	+	0.187716i
$515$	−3.89009e21			−0.786144
$516$		0			0
$517$		−	1.70006e21i		−	0.333074i
$518$	1.14974e22	+	3.84881e21i	2.21800	+	0.742486i
$519$		0			0
$520$	1.93146e21	+	2.81288e21i	0.361293	+	0.526167i
$521$	−4.04183e21			−0.744520			−0.372260	−	0.928129i	$-0.621417\pi$
$521$	−4.04183e21			−0.744520			−0.372260	+	0.928129i	$0.621417\pi$
$522$		0			0
$523$	5.82231e21			1.04012			0.520058	−	0.854131i	$-0.325910\pi$
$523$	5.82231e21			1.04012			0.520058	+	0.854131i	$0.325910\pi$
$524$	1.69592e21	+	1.27873e21i	0.298371	+	0.224972i
$525$		0			0
$526$	1.71886e21	−	5.13470e21i	0.293329	−	0.876253i
$527$			1.24644e22i			2.09502i
$528$		0			0
$529$	7.53376e20			0.122848
$530$	1.18177e21	+	3.95604e20i	0.189814	+	0.0635409i
$531$		0			0
$532$	7.13347e20	−	9.46082e20i	0.111175	−	0.147447i
$533$		−	6.58621e19i		−	0.0101115i
$534$		0			0
$535$			6.41196e21i			0.955345i
$536$	−8.36560e20	−	1.21832e21i	−0.122794	−	0.178831i
$537$		0			0
$538$	−2.81700e21	+	8.41513e21i	−0.401355	+	1.19895i
$539$	6.03296e21			0.846878
$540$		0			0
$541$		−	3.05007e21i		−	0.415654i	−0.978166	−	0.207827i	$-0.933361\pi$
$541$		−	3.05007e21i		−	0.415654i	0.978166	−	0.207827i	$-0.0666391\pi$
$542$	−1.45858e21	+	4.35718e21i	−0.195856	+	0.585074i
$543$		0			0
$544$	−6.30600e20	+	1.42102e22i	−0.0822172	+	1.85272i
$545$	−1.30525e22			−1.67696
$546$		0			0
$547$	−9.94165e21			−1.24039			−0.620197	−	0.784446i	$-0.712947\pi$
$547$	−9.94165e21			−1.24039			−0.620197	+	0.784446i	$0.712947\pi$
$548$	−9.17225e21	−	6.91590e21i	−1.12780	−	0.850363i
$549$		0			0
$550$	5.79486e21	+	1.93985e21i	0.692056	+	0.231669i
$551$			5.92049e20i			0.0696859i
$552$		0			0
$553$	−1.70163e22			−1.94564
$554$	−1.53769e21	+	4.59350e21i	−0.173297	+	0.517685i
$555$		0			0
$556$	−3.26762e21	−	2.46379e21i	−0.357794	−	0.269778i
$557$		−	1.20851e22i		−	1.30440i	−0.758048	−	0.652199i	$-0.773847\pi$
$557$		−	1.20851e22i		−	1.30440i	0.758048	−	0.652199i	$-0.226153\pi$
$558$		0			0
$559$		−	8.36411e20i		−	0.0877254i
$560$	5.63329e21	+	1.96881e22i	0.582449	+	2.03563i
$561$		0			0
$562$	7.27652e21	+	2.43585e21i	0.731195	+	0.244771i
$563$	−1.12872e22			−1.11820			−0.559100	−	0.829100i	$-0.688853\pi$
$563$	−1.12872e22			−1.11820			−0.559100	+	0.829100i	$0.688853\pi$
$564$		0			0
$565$			9.81692e21i			0.945339i
$566$	−7.22810e21	−	2.41964e21i	−0.686266	−	0.229731i
$567$		0			0
$568$	8.34018e21	−	5.72679e21i	0.769820	−	0.528597i
$569$	−5.86823e21			−0.534083			−0.267042	−	0.963685i	$-0.586046\pi$
$569$	−5.86823e21			−0.534083			−0.267042	+	0.963685i	$0.586046\pi$
$570$		0			0
$571$	−1.37932e22			−1.22061			−0.610304	−	0.792168i	$-0.708953\pi$
$571$	−1.37932e22			−1.22061			−0.610304	+	0.792168i	$0.708953\pi$
$572$	−2.17434e21	+	2.88373e21i	−0.189740	+	0.251644i
$573$		0			0
$574$	1.25475e20	−	3.74829e20i	0.0106479	−	0.0318081i
$575$		−	1.15926e22i		−	0.970151i
$576$		0			0
$577$	−2.09216e22			−1.70290			−0.851449	−	0.524437i	$-0.824276\pi$
$577$	−2.09216e22			−1.70290			−0.851449	+	0.524437i	$0.824276\pi$
$578$	2.88157e22	+	9.64617e21i	2.31316	+	0.774341i
$579$		0			0
$580$	−8.17015e21	−	6.16031e21i	−0.637978	−	0.481037i
$581$			1.41156e22i			1.08716i
$582$		0			0
$583$			1.31907e21i			0.0988373i
$584$	−1.12928e22	−	1.64462e22i	−0.834638	−	1.21552i
$585$		0			0
$586$	2.61515e20	−	7.81216e20i	0.0188068	−	0.0561811i
$587$	1.05244e22			0.746608			0.373304	−	0.927709i	$-0.378225\pi$
$587$	1.05244e22			0.746608			0.373304	+	0.927709i	$0.378225\pi$
$588$		0			0
$589$			2.03630e21i			0.140579i
$590$	9.41815e21	−	2.81345e22i	0.641430	−	1.91612i
$591$		0			0
$592$	−2.28613e22	+	6.54124e21i	−1.51540	+	0.433597i
$593$	1.40079e22			0.916085			0.458042	−	0.888930i	$-0.348551\pi$
$593$	1.40079e22			0.916085			0.458042	+	0.888930i	$0.348551\pi$
$594$		0			0
$595$	6.16821e22			3.92666
$596$	−7.85590e21	+	1.04189e22i	−0.493430	+	0.654415i
$597$		0			0
$598$	6.49697e21	+	2.17489e21i	0.397284	+	0.132993i
$599$			1.63288e22i			0.985233i	0.870247	+	0.492616i	$0.163959\pi$
$599$			1.63288e22i			0.985233i	−0.870247	+	0.492616i	$0.836041\pi$
$600$		0			0
$601$	−9.56729e20			−0.0562074			−0.0281037	−	0.999605i	$-0.508947\pi$
$601$	−9.56729e20			−0.0562074			−0.0281037	+	0.999605i	$0.508947\pi$
$602$	1.59347e21	−	4.76011e21i	0.0923786	−	0.275959i
$603$		0			0
$604$	−3.73081e21	+	4.94801e21i	−0.210624	+	0.279341i
$605$		−	1.28981e22i		−	0.718595i
$606$		0			0
$607$		−	3.42389e22i		−	1.85785i	−0.370273	−	0.928923i	$-0.620736\pi$
$607$		−	3.42389e22i		−	1.85785i	0.370273	−	0.928923i	$-0.379264\pi$
$608$	−1.03020e20	+	2.32151e21i	−0.00551689	+	0.124320i
$609$		0			0
$610$	1.12407e21	+	3.76286e20i	0.0586345	+	0.0196281i
$611$	4.10767e21			0.211478
$612$		0			0
$613$			3.27644e22i			1.64330i	0.569990	+	0.821652i	$0.306947\pi$
$613$			3.27644e22i			1.64330i	−0.569990	+	0.821652i	$0.693053\pi$
$614$	1.41281e22	+	4.72942e21i	0.699416	+	0.234132i
$615$		0			0
$616$	−1.78683e22	+	1.22693e22i	−0.861861	+	0.591797i
$617$	2.90372e21			0.138253			0.0691264	−	0.997608i	$-0.477979\pi$
$617$	2.90372e21			0.138253			0.0691264	+	0.997608i	$0.477979\pi$
$618$		0			0
$619$	2.23150e22			1.03531			0.517657	−	0.855588i	$-0.326804\pi$
$619$	2.23150e22			1.03531			0.517657	+	0.855588i	$0.326804\pi$
$620$	−2.81005e22	−	2.11878e22i	−1.28700	−	0.970404i
$621$		0			0
$622$	8.47233e21	−	2.53091e22i	0.378163	−	1.12968i
$623$		−	2.00501e22i		−	0.883513i
$624$		0			0
$625$	−2.24181e22			−0.962852
$626$	−3.89280e22	−	1.30313e22i	−1.65070	−	0.552578i
$627$		0			0
$628$	−2.78509e21	+	3.69374e21i	−0.115123	+	0.152683i
$629$			7.16237e22i			2.92315i
$630$		0			0
$631$		−	2.79894e22i		−	1.11368i	−0.830621	−	0.556838i	$-0.812014\pi$
$631$		−	2.79894e22i		−	1.11368i	0.830621	−	0.556838i	$-0.187986\pi$
$632$	2.75112e22	−	1.88906e22i	1.08087	−	0.742179i
$633$		0			0
$634$	9.23672e20	−	2.75925e21i	0.0353837	−	0.105701i
$635$	−7.98913e20			−0.0302211
$636$		0			0
$637$			1.45767e22i			0.537706i
$638$	3.43801e21	−	1.02703e22i	0.125240	−	0.374124i
$639$		0			0
$640$	−3.09643e22	−	2.55771e22i	−1.10007	−	0.908680i
$641$	2.28901e21			0.0803125			0.0401563	−	0.999193i	$-0.487214\pi$
$641$	2.28901e21			0.0803125			0.0401563	+	0.999193i	$0.487214\pi$
$642$		0			0
$643$	3.53144e22			1.20855			0.604274	−	0.796777i	$-0.293463\pi$
$643$	3.53144e22			1.20855			0.604274	+	0.796777i	$0.293463\pi$
$644$	3.28316e22	+	2.47551e22i	1.10970	+	0.836714i
$645$		0			0
$646$	6.63745e21	+	2.22191e21i	0.218847	+	0.0732600i
$647$		−	5.78292e22i		−	1.88327i	−0.336634	−	0.941636i	$-0.609288\pi$
$647$		−	5.78292e22i		−	1.88327i	0.336634	−	0.941636i	$-0.390712\pi$
$648$		0			0
$649$	3.14032e22			0.997739
$650$	−4.68704e21	+	1.40014e22i	−0.147093	+	0.439406i
$651$		0			0
$652$	1.22698e22	+	9.25149e21i	0.375715	+	0.283290i
$653$		−	4.75473e22i		−	1.43820i	−0.694904	−	0.719102i	$-0.744553\pi$
$653$		−	4.75473e22i		−	1.43820i	0.694904	−	0.719102i	$-0.255447\pi$
$654$		0			0
$655$			1.80636e22i			0.533181i
$656$	2.13252e20	+	7.45303e20i	0.00621815	+	0.0217321i
$657$		0			0
$658$	2.33772e22	+	7.82562e21i	0.665251	+	0.222695i
$659$	−1.20594e22			−0.339035			−0.169517	−	0.985527i	$-0.554221\pi$
$659$	−1.20594e22			−0.339035			−0.169517	+	0.985527i	$0.554221\pi$
$660$		0			0
$661$		−	1.63382e22i		−	0.448326i	−0.974552	−	0.224163i	$-0.928035\pi$
$661$		−	1.63382e22i		−	0.448326i	0.974552	−	0.224163i	$-0.0719648\pi$
$662$	1.05442e21	+	3.52973e20i	0.0285859	+	0.00956924i
$663$		0			0
$664$	−1.56704e22	−	2.28216e22i	−0.414702	−	0.603950i
$665$	1.00769e22			0.263484
$666$		0			0
$667$	−2.05457e22			−0.524462
$668$	−3.91337e22	+	5.19013e22i	−0.987050	+	1.30908i
$669$		0			0
$670$	3.98985e21	−	1.19187e22i	0.0982557	−	0.293516i
$671$			1.25466e21i			0.0305314i
$672$		0			0
$673$	−6.92380e22			−1.64522			−0.822610	−	0.568607i	$-0.807483\pi$
$673$	−6.92380e22			−1.64522			−0.822610	+	0.568607i	$0.807483\pi$
$674$	1.30795e22	+	4.37842e21i	0.307123	+	0.102811i
$675$		0			0
$676$	2.78524e22	+	2.10007e22i	0.638688	+	0.481572i
$677$		−	5.05127e22i		−	1.14470i	−0.820010	−	0.572350i	$-0.806032\pi$
$677$		−	5.05127e22i		−	1.14470i	0.820010	−	0.572350i	$-0.193968\pi$
$678$		0			0
$679$		−	9.01851e22i		−	1.99607i
$680$	−9.97250e22	+	6.84762e22i	−2.18139	+	1.49785i
$681$		0			0
$682$	1.18247e22	−	3.53236e22i	0.252648	−	0.754727i
$683$	6.89980e22			1.45704			0.728519	−	0.685025i	$-0.240209\pi$
$683$	6.89980e22			1.45704			0.728519	+	0.685025i	$0.240209\pi$
$684$		0			0
$685$		−	9.76957e22i		−	2.01535i
$686$	−4.66760e21	+	1.39434e22i	−0.0951701	+	0.284299i
$687$		0			0
$688$	2.70817e21	+	9.46493e21i	0.0539472	+	0.188543i
$689$	−3.18713e21			−0.0627546
$690$		0			0
$691$	1.01417e23			1.95114			0.975569	−	0.219694i	$-0.0705059\pi$
$691$	1.01417e23			1.95114			0.975569	+	0.219694i	$0.0705059\pi$
$692$	−1.81539e22	+	2.40768e22i	−0.345241	+	0.457878i
$693$		0			0
$694$	−2.45214e20	−	8.20863e19i	−0.00455690	−	0.00152544i
$695$		−	3.48041e22i		−	0.639370i
$696$		0			0
$697$	2.33501e21			0.0419205
$698$	1.37112e22	−	4.09590e22i	0.243350	−	0.726952i
$699$		0			0
$700$	−5.33490e22	+	7.07544e22i	−0.925426	+	1.22735i
$701$			3.43490e22i			0.589075i	0.955640	+	0.294537i	$0.0951655\pi$
$701$			3.43490e22i			0.589075i	−0.955640	+	0.294537i	$0.904834\pi$
$702$		0			0
$703$			1.17011e22i			0.196148i
$704$	1.52680e22	−	3.96729e22i	0.253047	−	0.657525i
$705$		0			0
$706$	6.89760e22	+	2.30900e22i	1.11753	+	0.374099i
$707$	1.70246e23			2.72723
$708$		0			0
$709$			5.45976e22i			0.855074i	0.903998	+	0.427537i	$0.140619\pi$
$709$			5.45976e22i			0.855074i	−0.903998	+	0.427537i	$0.859381\pi$
$710$	8.15914e22	+	2.73130e22i	1.26351	+	0.422964i
$711$		0			0
$712$	2.22586e22	+	3.24162e22i	0.337022	+	0.490820i
$713$	−7.06650e22			−1.05801
$714$		0			0
$715$	−3.07152e22			−0.449682
$716$	7.70672e22	+	5.81088e22i	1.11575	+	0.841275i
$717$		0			0
$718$	−1.66279e22	+	4.96719e22i	−0.235419	+	0.703260i
$719$			3.00804e22i			0.421165i	0.977576	+	0.210583i	$0.0675361\pi$
$719$			3.00804e22i			0.421165i	−0.977576	+	0.210583i	$0.932464\pi$
$720$		0			0
$721$	5.97065e22			0.817598
$722$	−6.89375e22	−	2.30771e22i	−0.933593	−	0.312524i
$723$		0			0
$724$	−2.60728e22	+	3.45792e22i	−0.345365	+	0.458043i
$725$		−	4.42775e22i		−	0.580068i
$726$		0			0
$727$			1.19550e23i			1.53206i	0.642806	+	0.766029i	$0.277770\pi$
$727$			1.19550e23i			1.53206i	−0.642806	+	0.766029i	$0.722230\pi$
$728$	−2.96448e22	−	4.31730e22i	−0.375748	−	0.547220i
$729$		0			0
$730$	5.38592e22	−	1.60892e23i	0.667847	−	1.99504i
$731$	2.96533e22			0.363692
$732$		0			0
$733$		−	3.41068e22i		−	0.409270i	−0.978838	−	0.204635i	$-0.934399\pi$
$733$		−	3.41068e22i		−	0.409270i	0.978838	−	0.204635i	$-0.0656007\pi$
$734$	−8.20149e21	+	2.45000e22i	−0.0973474	+	0.290803i
$735$		0			0
$736$	−8.05625e22	−	3.57508e21i	−0.935643	−	0.0415206i
$737$	1.33035e22			0.152836
$738$		0			0
$739$	−4.42548e22			−0.497513			−0.248757	−	0.968566i	$-0.580022\pi$
$739$	−4.42548e22			−0.497513			−0.248757	+	0.968566i	$0.580022\pi$
$740$	−1.61472e23	−	1.21750e23i	−1.79574	−	1.35399i
$741$		0			0
$742$	−1.81383e22	−	6.07187e21i	−0.197408	−	0.0660833i
$743$		−	6.24045e21i		−	0.0671901i	−0.999436	−	0.0335951i	$-0.989304\pi$
$743$		−	6.24045e21i		−	0.0671901i	0.999436	−	0.0335951i	$-0.0106957\pi$
$744$		0			0
$745$	−1.10974e23			−1.16942
$746$	−5.26880e22	+	1.57393e23i	−0.549289	+	1.64087i
$747$		0			0
$748$	−1.02237e23	−	7.70869e22i	−1.04327	−	0.786625i
$749$		−	9.84131e22i		−	0.993570i
$750$		0			0
$751$			3.46827e22i			0.342762i	0.985205	+	0.171381i	$0.0548229\pi$
$751$			3.46827e22i			0.342762i	−0.985205	+	0.171381i	$0.945177\pi$
$752$	−4.64829e22	+	1.33000e22i	−0.454517	+	0.130050i
$753$		0			0
$754$	2.48148e22	+	8.30687e21i	0.237542	+	0.0795182i
$755$	−5.27024e22			−0.499177
$756$		0			0
$757$		−	3.91438e22i		−	0.362991i	−0.983392	−	0.181495i	$-0.941906\pi$
$757$		−	3.91438e22i		−	0.362991i	0.983392	−	0.181495i	$-0.0580938\pi$
$758$	1.09192e21	+	3.65524e20i	0.0100193	+	0.00335400i
$759$		0			0
$760$	−1.62919e22	+	1.11869e22i	−0.146374	+	0.100508i
$761$	7.00706e22			0.622958			0.311479	−	0.950253i	$-0.399176\pi$
$761$	7.00706e22			0.622958			0.311479	+	0.950253i	$0.399176\pi$
$762$		0			0
$763$	2.00335e23			1.74405
$764$	6.05386e22	−	8.02898e22i	0.521538	−	0.691693i
$765$		0			0
$766$	−4.49781e22	+	1.34362e23i	−0.379464	+	1.13356i
$767$			7.58760e22i			0.633492i
$768$		0			0
$769$	−3.23281e22			−0.264344			−0.132172	−	0.991227i	$-0.542195\pi$
$769$	−3.23281e22			−0.264344			−0.132172	+	0.991227i	$0.542195\pi$
$770$	−1.74804e23	−	5.85164e22i	−1.41457	−	0.473534i
$771$		0			0
$772$	3.96756e21	+	2.99154e21i	0.0314474	+	0.0237114i
$773$			1.25542e23i			0.984809i	0.870366	+	0.492405i	$0.163882\pi$
$773$			1.25542e23i			0.984809i	−0.870366	+	0.492405i	$0.836118\pi$
$774$		0			0
$775$		−	1.52288e23i		−	1.17018i
$776$	1.00119e23	+	1.45808e23i	0.761416	+	1.10888i
$777$		0			0
$778$	−1.22884e21	+	3.67088e21i	−0.00915503	+	0.0273485i
$779$	3.81468e20			0.00281292
$780$		0			0
$781$			9.10708e22i			0.657917i
$782$	−7.71064e22	+	2.30337e23i	−0.551361	+	1.64706i
$783$		0			0
$784$	−4.71973e22	−	1.64952e23i	−0.330666	−	1.15566i
$785$	−3.93428e22			−0.272840
$786$		0			0
$787$	1.23669e22			0.0840353			0.0420176	−	0.999117i	$-0.486621\pi$
$787$	1.23669e22			0.0840353			0.0420176	+	0.999117i	$0.486621\pi$
$788$	3.84121e22	−	5.09443e22i	0.258380	−	0.342678i
$789$		0			0
$790$	2.69140e23	+	9.00957e22i	1.77403	+	0.593864i
$791$		−	1.50674e23i		−	0.983163i
$792$		0			0
$793$	−3.03149e21			−0.0193852
$794$	5.25515e22	−	1.56985e23i	0.332676	−	0.993791i
$795$		0			0
$796$	3.49990e22	−	4.64177e22i	0.217146	−	0.287991i
$797$		−	2.33288e23i		−	1.43294i	−0.697620	−	0.716468i	$-0.745758\pi$
$797$		−	2.33288e23i		−	1.43294i	0.697620	−	0.716468i	$-0.254242\pi$
$798$		0			0
$799$			1.45629e23i			0.876747i
$800$	7.70456e21	−	1.73618e23i	0.0459227	−	1.03484i
$801$		0			0
$802$	−5.73786e22	−	1.92077e22i	−0.335239	−	0.112223i
$803$	1.79585e23			1.03883
$804$		0			0
$805$			3.49696e23i			1.98301i
$806$	8.53483e22	+	2.85707e22i	0.479197	+	0.160413i
$807$		0			0
$808$	−2.75247e23	+	1.88999e23i	−1.51507	+	1.04032i
$809$	−1.68226e22			−0.0916865			−0.0458433	−	0.998949i	$-0.514597\pi$
$809$	−1.68226e22			−0.0916865			−0.0458433	+	0.998949i	$0.514597\pi$
$810$		0			0
$811$	−2.04733e22			−0.109401			−0.0547004	−	0.998503i	$-0.517420\pi$
$811$	−2.04733e22			−0.109401			−0.0547004	+	0.998503i	$0.517420\pi$
$812$	1.25398e23	+	9.45507e22i	0.663505	+	0.500284i
$813$		0			0
$814$	6.79477e22	−	2.02978e23i	0.352517	−	1.05306i
$815$			1.30689e23i			0.671394i
$816$		0			0
$817$	4.84442e21			0.0244043
$818$	2.66776e23	+	8.93045e22i	1.33082	+	0.445499i
$819$		0			0
$820$	−3.96919e21	+	5.26417e21i	−0.0194174	+	0.0257525i
$821$			2.90138e23i			1.40559i	0.711392	+	0.702795i	$0.248065\pi$
$821$			2.90138e23i			1.40559i	−0.711392	+	0.702795i	$0.751935\pi$
$822$		0			0
$823$		−	3.39906e23i		−	1.61495i	−0.589900	−	0.807476i	$-0.700833\pi$
$823$		−	3.39906e23i		−	1.61495i	0.589900	−	0.807476i	$-0.299167\pi$
$824$	−9.65310e22	+	6.62831e22i	−0.454202	+	0.311878i
$825$		0			0
$826$	−1.44553e23	+	4.31819e23i	−0.667094	+	1.99279i
$827$	−2.71198e23			−1.23949			−0.619745	−	0.784803i	$-0.712764\pi$
$827$	−2.71198e23			−1.23949			−0.619745	+	0.784803i	$0.712764\pi$
$828$		0			0
$829$		−	2.18126e23i		−	0.977848i	−0.872326	−	0.488924i	$-0.837389\pi$
$829$		−	2.18126e23i		−	0.977848i	0.872326	−	0.488924i	$-0.162611\pi$
$830$	7.47378e22	−	2.23262e23i	0.331830	−	0.991264i
$831$		0			0
$832$	9.58569e22	+	3.68903e22i	0.417481	+	0.160667i
$833$	−5.16790e23			−2.22923
$834$		0			0
$835$	−5.52812e23			−2.33930
$836$	−1.67023e22	−	1.25936e22i	−0.0700047	−	0.0527837i
$837$		0			0
$838$	1.42649e22	+	4.77524e21i	0.0586566	+	0.0196355i
$839$			9.38513e22i			0.382248i	0.981566	+	0.191124i	$0.0612132\pi$
$839$			9.38513e22i			0.382248i	−0.981566	+	0.191124i	$0.938787\pi$
$840$		0			0
$841$	1.71773e23			0.686416
$842$	7.06032e22	−	2.10911e23i	0.279465	−	0.834837i
$843$		0			0
$844$	9.51640e21	+	7.17539e21i	0.0369601	+	0.0278680i
$845$			2.96662e23i			1.14132i
$846$		0			0
$847$			1.97966e23i			0.747347i
$848$	3.60659e22	−	1.03194e22i	0.134875	−	0.0385913i
$849$		0			0
$850$	−4.96393e23	−	1.66170e23i	−1.82169	−	0.609819i
$851$	−4.06058e23			−1.47622
$852$		0			0
$853$		−	1.61571e23i		−	0.576462i	−0.957561	−	0.288231i	$-0.906933\pi$
$853$		−	1.61571e23i		−	0.576462i	0.957561	−	0.288231i	$-0.0930670\pi$
$854$	−1.72526e22	−	5.77537e21i	−0.0609805	−	0.0204135i
$855$		0			0
$856$	1.09253e23	+	1.59110e23i	0.379004	+	0.551960i
$857$	3.29920e23			1.13387			0.566933	−	0.823764i	$-0.308130\pi$
$857$	3.29920e23			1.13387			0.566933	+	0.823764i	$0.308130\pi$
$858$		0			0
$859$	3.82694e23			1.29094			0.645470	−	0.763785i	$-0.276661\pi$
$859$	3.82694e23			1.29094			0.645470	+	0.763785i	$0.276661\pi$
$860$	−5.04065e22	+	6.68520e22i	−0.168461	+	0.223422i
$861$		0			0
$862$	1.56519e22	−	4.67565e22i	0.0513464	−	0.153385i
$863$		−	4.07008e23i		−	1.32287i	−0.750003	−	0.661435i	$-0.769948\pi$
$863$		−	4.07008e23i		−	1.32287i	0.750003	−	0.661435i	$-0.230052\pi$
$864$		0			0
$865$	−2.56447e23			−0.818217
$866$	−5.69964e22	−	1.90798e22i	−0.180179	−	0.0603156i
$867$		0			0
$868$	4.31296e23	+	3.25198e23i	1.33850	+	1.00923i
$869$			3.00409e23i			0.923751i
$870$		0			0
$871$			3.21436e22i			0.0970398i
$872$	−3.23893e23	+	2.22401e23i	−0.968878	+	0.665280i
$873$		0			0
$874$	−1.25968e22	+	3.76299e22i	−0.0369971	+	0.110520i
$875$	−2.60908e22			−0.0759317
$876$		0			0
$877$			4.28239e23i			1.22374i	0.790958	+	0.611871i	$0.209583\pi$
$877$			4.28239e23i			1.22374i	−0.790958	+	0.611871i	$0.790417\pi$
$878$	1.77576e23	−	5.30466e23i	0.502837	−	1.50211i
$879$		0			0
$880$	3.47578e23	−	9.94514e22i	0.966474	−	0.276535i
$881$	3.65451e23			1.00698			0.503491	−	0.864000i	$-0.332049\pi$
$881$	3.65451e23			1.00698			0.503491	+	0.864000i	$0.332049\pi$
$882$		0			0
$883$	−4.78165e23			−1.29387			−0.646937	−	0.762543i	$-0.723950\pi$
$883$	−4.78165e23			−1.29387			−0.646937	+	0.762543i	$0.723950\pi$
$884$	1.86256e23	−	2.47023e23i	0.499450	−	0.662399i
$885$		0			0
$886$	−2.60198e23	−	8.71025e22i	−0.685227	−	0.229383i
$887$			4.68950e23i			1.22388i	0.790905	+	0.611939i	$0.209610\pi$
$887$			4.68950e23i			1.22388i	−0.790905	+	0.611939i	$0.790390\pi$
$888$		0			0
$889$	1.22620e22			0.0314302
$890$	−1.06159e23	+	3.17125e23i	−0.269673	+	0.805584i
$891$		0			0
$892$	1.86673e23	−	2.47576e23i	0.465760	−	0.617717i
$893$			2.37913e22i			0.0588310i
$894$		0			0
$895$			8.20860e23i			1.99381i
$896$	4.75252e23	+	3.92566e23i	1.14409	+	0.945037i
$897$		0			0
$898$	2.66202e23	+	8.91123e22i	0.629507	+	0.210730i
$899$	−2.69901e23			−0.632597
$900$		0			0
$901$		−	1.12993e23i		−	0.260168i
$902$	−6.61731e21	−	2.21517e21i	−0.0151018	−	0.00505539i
$903$		0			0
$904$	1.67270e23	+	2.43603e23i	0.375034	+	0.546179i
$905$	−3.68310e23			−0.818513
$906$		0			0
$907$	−2.76998e22			−0.0604810			−0.0302405	−	0.999543i	$-0.509627\pi$
$907$	−2.76998e22			−0.0604810			−0.0302405	+	0.999543i	$0.509627\pi$
$908$	5.29717e23	+	3.99407e23i	1.14645	+	0.864429i
$909$		0			0
$910$	1.41386e23	−	4.22358e23i	0.300660	−	0.898153i
$911$			6.80989e23i			1.43547i	0.696318	+	0.717734i	$0.254820\pi$
$911$			6.80989e23i			1.43547i	−0.696318	+	0.717734i	$0.745180\pi$
$912$		0			0
$913$	2.49201e23			0.516158
$914$	−1.68129e23	−	5.62818e22i	−0.345201	−	0.115558i
$915$		0			0
$916$	4.89869e23	−	6.49691e23i	0.988362	−	1.31082i
$917$		−	2.77247e23i		−	0.554515i
$918$		0			0
$919$		−	4.10602e23i		−	0.807043i	−0.914970	−	0.403522i	$-0.867786\pi$
$919$		−	4.10602e23i		−	0.807043i	0.914970	−	0.403522i	$-0.132214\pi$
$920$	−3.88214e23	−	5.65374e23i	−0.756430	−	1.10162i
$921$		0			0
$922$	1.43290e23	−	4.28045e23i	0.274390	−	0.819676i
$923$	−2.20044e23			−0.417730
$924$		0			0
$925$		−	8.75085e23i		−	1.63274i
$926$	7.21891e22	−	2.15648e23i	0.133531	−	0.398894i
$927$		0			0
$928$	−3.07704e23	−	1.36548e22i	−0.559435	−	0.0248258i
$929$	5.97517e23			1.07702			0.538511	−	0.842618i	$-0.318987\pi$
$929$	5.97517e23			1.07702			0.538511	+	0.842618i	$0.318987\pi$
$930$		0			0
$931$	−8.44273e22			−0.149584
$932$	5.03923e23	+	3.79959e23i	0.885192	+	0.667436i
$933$		0			0
$934$	−5.87886e23	−	1.96797e23i	−1.01512	−	0.339816i
$935$		−	1.08895e24i		−	1.86429i
$936$		0			0
$937$	7.64808e22			0.128717			0.0643585	−	0.997927i	$-0.479500\pi$
$937$	7.64808e22			0.128717			0.0643585	+	0.997927i	$0.479500\pi$
$938$	−6.12376e22	+	1.82933e23i	−0.102187	+	0.305260i
$939$		0			0
$940$	−3.28314e23	−	2.47550e23i	−0.538601	−	0.406106i
$941$		−	9.30929e23i		−	1.51426i	−0.653266	−	0.757129i	$-0.726601\pi$
$941$		−	9.30929e23i		−	1.51426i	0.653266	−	0.757129i	$-0.273399\pi$
$942$		0			0
$943$			1.32380e22i			0.0211703i
$944$	−2.45675e23	−	8.58622e23i	−0.389570	−	1.36153i
$945$		0			0
$946$	−8.40361e22	−	2.81314e22i	−0.131020	−	0.0438594i
$947$	2.38672e23			0.368979			0.184489	−	0.982835i	$-0.440937\pi$
$947$	2.38672e23			0.368979			0.184489	+	0.982835i	$0.440937\pi$
$948$		0			0
$949$			4.33909e23i			0.659582i
$950$	−8.10952e22	−	2.71469e22i	−0.122238	−	0.0409197i
$951$		0			0
$952$	1.53062e24	−	1.05100e24i	2.26867	−	1.55778i
$953$	−8.09862e23			−1.19033			−0.595166	−	0.803603i	$-0.702914\pi$
$953$	−8.09862e23			−1.19033			−0.595166	+	0.803603i	$0.702914\pi$
$954$		0			0
$955$	8.55184e23			1.23604
$956$	4.62504e23	−	6.13398e23i	0.662906	−	0.879183i
$957$		0			0
$958$	2.36387e23	−	7.06151e23i	0.333196	−	0.995344i
$959$			1.49947e24i			2.09599i
$960$		0			0
$961$	−2.00877e23			−0.276148
$962$	4.90432e23	+	1.64174e23i	0.668618	+	0.223823i
$963$		0			0
$964$	−4.70501e23	−	3.54758e23i	−0.630876	−	0.475682i
$965$			4.22593e22i			0.0561958i
$966$		0			0
$967$		−	1.42829e24i		−	1.86812i	−0.357120	−	0.934059i	$-0.616241\pi$
$967$		−	1.42829e24i		−	1.86812i	0.357120	−	0.934059i	$-0.383759\pi$
$968$	−2.19771e23	−	3.20062e23i	−0.285080	−	0.415176i
$969$		0			0
$970$	−4.77501e23	+	1.42642e24i	−0.609257	+	1.82001i
$971$	−1.39310e24			−1.76290			−0.881451	−	0.472276i	$-0.843432\pi$
$971$	−1.39310e24			−1.76290			−0.881451	+	0.472276i	$0.843432\pi$
$972$		0			0
$973$			5.34187e23i			0.664952i
$974$	3.20498e23	−	9.57412e23i	0.395688	−	1.18203i
$975$		0			0
$976$	3.43048e22	−	9.81552e21i	0.0416635	−	0.0119211i
$977$	1.28434e24			1.54712			0.773561	−	0.633722i	$-0.218474\pi$
$977$	1.28434e24			1.54712			0.773561	+	0.633722i	$0.218474\pi$
$978$		0			0
$979$	−3.53970e23			−0.419473
$980$	8.78471e23	−	1.16508e24i	1.03257	−	1.36945i
$981$		0			0
$982$	1.58930e24	+	5.32025e23i	1.83787	+	0.615234i
$983$		−	6.92489e23i		−	0.794300i	−0.917754	−	0.397150i	$-0.869999\pi$
$983$		−	6.92489e23i		−	0.794300i	0.917754	−	0.397150i	$-0.130001\pi$
$984$		0			0
$985$	5.42619e23			0.612358
$986$	−2.94504e23	+	8.79761e23i	−0.329667	+	0.984803i
$987$		0			0
$988$	3.04284e22	−	4.03559e22i	0.0335138	−	0.0444479i
$989$			1.68114e23i			0.183669i
$990$		0			0
$991$			1.54253e24i			1.65823i	0.559075	+	0.829117i	$0.311156\pi$
$991$			1.54253e24i			1.65823i	−0.559075	+	0.829117i	$0.688844\pi$
$992$	−1.05832e24	−	4.69645e22i	−1.12856	−	0.0500814i
$993$		0			0
$994$	−1.25229e24	−	4.19211e23i	−1.31406	−	0.439887i
$995$	4.94405e23			0.514633
$996$		0			0
$997$		−	1.85521e24i		−	1.90034i	−0.311726	−	0.950172i	$-0.600907\pi$
$997$		−	1.85521e24i		−	1.90034i	0.311726	−	0.950172i	$-0.399093\pi$
$998$	1.41908e24	+	4.75044e23i	1.44199	+	0.482714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.17.b.b.19.14		14
3.2	odd	2		8.17.d.b.3.1	✓	14
8.3	odd	2	inner	72.17.b.b.19.13		14
12.11	even	2		32.17.d.b.15.11		14
24.5	odd	2		32.17.d.b.15.12		14
24.11	even	2		8.17.d.b.3.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.1	✓	14	3.2	odd	2
8.17.d.b.3.2	yes	14	24.11	even	2
32.17.d.b.15.11		14	12.11	even	2
32.17.d.b.15.12		14	24.5	odd	2
72.17.b.b.19.13		14	8.3	odd	2	inner
72.17.b.b.19.14		14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(242.759 + 81.2647i) q^{2} +(52328.1 + 39455.5i) q^{4} +557358. i q^{5} -8.55454e6i q^{7} +(9.49679e6 + 1.38306e7i) q^{8} +O(q^{10})\)	\(q+(242.759 + 81.2647i) q^{2} +(52328.1 + 39455.5i) q^{4} +557358. i q^{5} -8.55454e6i q^{7} +(9.49679e6 + 1.38306e7i) q^{8} +(-4.52935e7 + 1.35304e8i) q^{10} -1.51024e8 q^{11} -3.64901e8i q^{13} +(6.95181e8 - 2.07669e9i) q^{14} +(1.18149e9 + 4.12926e9i) q^{16} +1.29368e10 q^{17} +2.11348e9 q^{19} +(-2.19908e10 + 2.91655e10i) q^{20} +(-3.66624e10 - 1.22729e10i) q^{22} +7.33433e10i q^{23} -1.58060e11 q^{25} +(2.96535e10 - 8.85830e10i) q^{26} +(3.37523e11 - 4.47643e11i) q^{28} +2.80131e11i q^{29} +9.63483e11i q^{31} +(-4.87445e10 + 1.09843e12i) q^{32} +(3.14054e12 + 1.05131e12i) q^{34} +4.76794e12 q^{35} +5.53641e12i q^{37} +(5.13066e11 + 1.71751e11i) q^{38} +(-7.70860e12 + 5.29311e12i) q^{40} +1.80493e11 q^{41} +2.29216e12 q^{43} +(-7.90278e12 - 5.95871e12i) q^{44} +(-5.96022e12 + 1.78048e13i) q^{46} +1.12569e13i q^{47} -3.99471e13 q^{49} +(-3.83705e13 - 1.28447e13i) q^{50} +(1.43973e13 - 1.90946e13i) q^{52} -8.73423e12i q^{53} -8.41742e13i q^{55} +(1.18314e14 - 8.12407e13i) q^{56} +(-2.27647e13 + 6.80043e13i) q^{58} -2.07936e14 q^{59} -8.30772e12i q^{61} +(-7.82971e13 + 2.33894e14i) q^{62} +(-1.01097e14 + 2.62693e14i) q^{64} +2.03380e14 q^{65} -8.80887e13 q^{67} +(6.76960e14 + 5.10429e14i) q^{68} +(1.15746e15 + 3.87465e14i) q^{70} -6.03023e14i q^{71} -1.18912e15 q^{73} +(-4.49915e14 + 1.34401e15i) q^{74} +(1.10594e14 + 8.33882e13i) q^{76} +1.29194e15i q^{77} -1.98915e15i q^{79} +(-2.30148e15 + 6.58515e14i) q^{80} +(4.38164e13 + 1.46677e13i) q^{82} -1.65008e15 q^{83} +7.21045e15i q^{85} +(5.56443e14 + 1.86272e14i) q^{86} +(-1.43424e15 - 2.08875e15i) q^{88} +2.34380e15 q^{89} -3.12156e15 q^{91} +(-2.89380e15 + 3.83791e15i) q^{92} +(-9.14792e14 + 2.73273e15i) q^{94} +1.17796e15i q^{95} +1.05424e16 q^{97} +(-9.69754e15 - 3.24629e15i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 350 q^{2} - 54220 q^{4} - 10899160 q^{8}+O(q^{10}) \) 14 * q + 350 * q^2 - 54220 * q^4 - 10899160 * q^8	\( 14 q + 350 q^{2} - 54220 q^{4} - 10899160 q^{8} + 87155280 q^{10} + 49140292 q^{11} + 2675193504 q^{14} + 9716374544 q^{16} + 9985136356 q^{17} + 62922133180 q^{19} - 31953450720 q^{20} - 51493048676 q^{22} - 429906632050 q^{25} + 518273679696 q^{26} + 102542376000 q^{28} - 95751080800 q^{32} + 1015818512644 q^{34} + 3057653406720 q^{35} - 9010383442844 q^{38} - 4027933291200 q^{40} - 8719629072668 q^{41} + 16716309178300 q^{43} + 4351929975880 q^{44} + 21043605267744 q^{46} - 104740771400434 q^{49} + 54483696687710 q^{50} - 73249356722400 q^{52} - 110873799752064 q^{56} + 256627273576560 q^{58} - 347007330293180 q^{59} - 346701622780800 q^{62} - 332173589517760 q^{64} - 220877370432000 q^{65} - 614258765968196 q^{67} + 12\!\cdots\!76 q^{68}+ \cdots - 34\!\cdots\!30 q^{98}+O(q^{100}) \) 14 * q + 350 * q^2 - 54220 * q^4 - 10899160 * q^8 + 87155280 * q^10 + 49140292 * q^11 + 2675193504 * q^14 + 9716374544 * q^16 + 9985136356 * q^17 + 62922133180 * q^19 - 31953450720 * q^20 - 51493048676 * q^22 - 429906632050 * q^25 + 518273679696 * q^26 + 102542376000 * q^28 - 95751080800 * q^32 + 1015818512644 * q^34 + 3057653406720 * q^35 - 9010383442844 * q^38 - 4027933291200 * q^40 - 8719629072668 * q^41 + 16716309178300 * q^43 + 4351929975880 * q^44 + 21043605267744 * q^46 - 104740771400434 * q^49 + 54483696687710 * q^50 - 73249356722400 * q^52 - 110873799752064 * q^56 + 256627273576560 * q^58 - 347007330293180 * q^59 - 346701622780800 * q^62 - 332173589517760 * q^64 - 220877370432000 * q^65 - 614258765968196 * q^67 + 1235787871965976 * q^68 - 442172390987520 * q^70 - 542888518370276 * q^73 - 2394643836493776 * q^74 - 614792000883272 * q^76 - 6402194304908160 * q^80 + 4810720063300804 * q^82 - 7362421930746044 * q^83 + 8963192329247716 * q^86 + 3396904358318224 * q^88 + 408131327364580 * q^89 - 7162887702930432 * q^91 + 9213856910218560 * q^92 - 15838781433150144 * q^94 + 18372136634257180 * q^97 - 34005570793293730 * q^98

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