LMFDB - Embedded newform 128.12.e.b.33.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,12,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$98.3479271116$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.7
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-221.481 - 221.481i) q^{3} +(7918.20 - 7918.20i) q^{5} +76836.1i q^{7} -79039.1i q^{9} +O(q^{10})$	\(q+(-221.481 - 221.481i) q^{3} +(7918.20 - 7918.20i) q^{5} +76836.1i q^{7} -79039.1i q^{9} +(197951. - 197951. i) q^{11} +(46856.2 + 46856.2i) q^{13} -3.50747e6 q^{15} +9.74414e6 q^{17} +(-2.85298e6 - 2.85298e6i) q^{19} +(1.70178e7 - 1.70178e7i) q^{21} +3.12758e7i q^{23} -7.65676e7i q^{25} +(-5.67404e7 + 5.67404e7i) q^{27} +(1.26920e8 + 1.26920e8i) q^{29} +3.46657e7 q^{31} -8.76847e7 q^{33} +(6.08404e8 + 6.08404e8i) q^{35} +(-2.25685e8 + 2.25685e8i) q^{37} -2.07555e7i q^{39} +4.55938e8i q^{41} +(-7.03132e8 + 7.03132e8i) q^{43} +(-6.25847e8 - 6.25847e8i) q^{45} +6.32523e8 q^{47} -3.92646e9 q^{49} +(-2.15814e9 - 2.15814e9i) q^{51} +(1.37083e9 - 1.37083e9i) q^{53} -3.13483e9i q^{55} +1.26376e9i q^{57} +(-1.10533e9 + 1.10533e9i) q^{59} +(-3.14198e9 - 3.14198e9i) q^{61} +6.07306e9 q^{63} +7.42033e8 q^{65} +(3.21875e9 + 3.21875e9i) q^{67} +(6.92700e9 - 6.92700e9i) q^{69} +1.72208e10i q^{71} +1.53135e10i q^{73} +(-1.69583e10 + 1.69583e10i) q^{75} +(1.52098e10 + 1.52098e10i) q^{77} +4.44888e10 q^{79} +1.11323e10 q^{81} +(1.61561e10 + 1.61561e10i) q^{83} +(7.71560e10 - 7.71560e10i) q^{85} -5.62207e10i q^{87} -1.60769e10i q^{89} +(-3.60024e9 + 3.60024e9i) q^{91} +(-7.67780e9 - 7.67780e9i) q^{93} -4.51809e10 q^{95} +7.16237e9 q^{97} +(-1.56458e10 - 1.56458e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 + 2 * q^5	$ 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−221.481	−	221.481i	−0.526223	−	0.526223i	0.393221	−	0.919444i	$-0.371361\pi$
$3$	−221.481	−	221.481i	−0.526223	−	0.526223i	−0.919444	+	0.393221i	$0.871361\pi$
$4$		0			0
$5$	7918.20	−	7918.20i	1.13316	−	1.13316i	0.143512	−	0.989649i	$-0.454161\pi$
$5$	7918.20	−	7918.20i	1.13316	−	1.13316i	0.989649	−	0.143512i	$-0.0458395\pi$
$6$		0			0
$7$			76836.1i			1.72793i	0.503552	+	0.863965i	$0.332026\pi$
$7$			76836.1i			1.72793i	−0.503552	+	0.863965i	$0.667974\pi$
$8$		0			0
$9$		−	79039.1i		−	0.446178i
$10$		0			0
$11$	197951.	−	197951.i	0.370593	−	0.370593i	−0.497100	−	0.867693i	$-0.665602\pi$
$11$	197951.	−	197951.i	0.370593	−	0.370593i	0.867693	+	0.497100i	$0.165602\pi$
$12$		0			0
$13$	46856.2	+	46856.2i	0.0350008	+	0.0350008i	0.724391	−	0.689390i	$-0.242121\pi$
$13$	46856.2	+	46856.2i	0.0350008	+	0.0350008i	−0.689390	+	0.724391i	$0.742121\pi$
$14$		0			0
$15$	−3.50747e6			−1.19259
$16$		0			0
$17$	9.74414e6			1.66446			0.832232	−	0.554428i	$-0.187063\pi$
$17$	9.74414e6			1.66446			0.832232	+	0.554428i	$0.187063\pi$
$18$		0			0
$19$	−2.85298e6	−	2.85298e6i	−0.264334	−	0.264334i	0.562478	−	0.826812i	$-0.309848\pi$
$19$	−2.85298e6	−	2.85298e6i	−0.264334	−	0.264334i	−0.826812	+	0.562478i	$0.809848\pi$
$20$		0			0
$21$	1.70178e7	−	1.70178e7i	0.909277	−	0.909277i
$22$		0			0
$23$			3.12758e7i			1.01322i	0.862174	+	0.506611i	$0.169102\pi$
$23$			3.12758e7i			1.01322i	−0.862174	+	0.506611i	$0.830898\pi$
$24$		0			0
$25$		−	7.65676e7i		−	1.56810i
$26$		0			0
$27$	−5.67404e7	+	5.67404e7i	−0.761013	+	0.761013i
$28$		0			0
$29$	1.26920e8	+	1.26920e8i	1.14905	+	1.14905i	0.986739	+	0.162315i	$0.0518961\pi$
$29$	1.26920e8	+	1.26920e8i	1.14905	+	1.14905i	0.162315	+	0.986739i	$0.448104\pi$
$30$		0			0
$31$	3.46657e7			0.217475			0.108738	−	0.994070i	$-0.465319\pi$
$31$	3.46657e7			0.217475			0.108738	+	0.994070i	$0.465319\pi$
$32$		0			0
$33$	−8.76847e7			−0.390029
$34$		0			0
$35$	6.08404e8	+	6.08404e8i	1.95802	+	1.95802i
$36$		0			0
$37$	−2.25685e8	+	2.25685e8i	−0.535048	+	0.535048i	−0.922070	−	0.387022i	$-0.873504\pi$
$37$	−2.25685e8	+	2.25685e8i	−0.535048	+	0.535048i	0.387022	+	0.922070i	$0.373504\pi$
$38$		0			0
$39$		−	2.07555e7i		−	0.0368365i
$40$		0			0
$41$			4.55938e8i			0.614603i	0.951612	+	0.307302i	$0.0994260\pi$
$41$			4.55938e8i			0.614603i	−0.951612	+	0.307302i	$0.900574\pi$
$42$		0			0
$43$	−7.03132e8	+	7.03132e8i	−0.729390	+	0.729390i	−0.970498	−	0.241108i	$-0.922489\pi$
$43$	−7.03132e8	+	7.03132e8i	−0.729390	+	0.729390i	0.241108	+	0.970498i	$0.422489\pi$
$44$		0			0
$45$	−6.25847e8	−	6.25847e8i	−0.505591	−	0.505591i
$46$		0			0
$47$	6.32523e8			0.402289			0.201144	−	0.979562i	$-0.435534\pi$
$47$	6.32523e8			0.402289			0.201144	+	0.979562i	$0.435534\pi$
$48$		0			0
$49$	−3.92646e9			−1.98574
$50$		0			0
$51$	−2.15814e9	−	2.15814e9i	−0.875880	−	0.875880i
$52$		0			0
$53$	1.37083e9	−	1.37083e9i	0.450263	−	0.450263i	−0.445179	−	0.895442i	$-0.646860\pi$
$53$	1.37083e9	−	1.37083e9i	0.450263	−	0.450263i	0.895442	+	0.445179i	$0.146860\pi$
$54$		0			0
$55$		−	3.13483e9i		−	0.839883i
$56$		0			0
$57$			1.26376e9i			0.278198i
$58$		0			0
$59$	−1.10533e9	+	1.10533e9i	−0.201282	+	0.201282i	−0.800549	−	0.599267i	$-0.795459\pi$
$59$	−1.10533e9	+	1.10533e9i	−0.201282	+	0.201282i	0.599267	+	0.800549i	$0.295459\pi$
$60$		0			0
$61$	−3.14198e9	−	3.14198e9i	−0.476310	−	0.476310i	0.427639	−	0.903949i	$-0.359345\pi$
$61$	−3.14198e9	−	3.14198e9i	−0.476310	−	0.476310i	−0.903949	+	0.427639i	$0.859345\pi$
$62$		0			0
$63$	6.07306e9			0.770965
$64$		0			0
$65$	7.42033e8			0.0793231
$66$		0			0
$67$	3.21875e9	+	3.21875e9i	0.291256	+	0.291256i	0.837576	−	0.546320i	$-0.183972\pi$
$67$	3.21875e9	+	3.21875e9i	0.291256	+	0.291256i	−0.546320	+	0.837576i	$0.683972\pi$
$68$		0			0
$69$	6.92700e9	−	6.92700e9i	0.533181	−	0.533181i
$70$		0			0
$71$			1.72208e10i			1.13275i	0.824148	+	0.566374i	$0.191654\pi$
$71$			1.72208e10i			1.13275i	−0.824148	+	0.566374i	$0.808346\pi$
$72$		0			0
$73$			1.53135e10i			0.864566i	0.901738	+	0.432283i	$0.142292\pi$
$73$			1.53135e10i			0.864566i	−0.901738	+	0.432283i	$0.857708\pi$
$74$		0			0
$75$	−1.69583e10	+	1.69583e10i	−0.825173	+	0.825173i
$76$		0			0
$77$	1.52098e10	+	1.52098e10i	0.640359	+	0.640359i
$78$		0			0
$79$	4.44888e10			1.62668			0.813340	−	0.581789i	$-0.197647\pi$
$79$	4.44888e10			1.62668			0.813340	+	0.581789i	$0.197647\pi$
$80$		0			0
$81$	1.11323e10			0.354747
$82$		0			0
$83$	1.61561e10	+	1.61561e10i	0.450201	+	0.450201i	0.895421	−	0.445220i	$-0.146874\pi$
$83$	1.61561e10	+	1.61561e10i	0.450201	+	0.450201i	−0.445220	+	0.895421i	$0.646874\pi$
$84$		0			0
$85$	7.71560e10	−	7.71560e10i	1.88610	−	1.88610i
$86$		0			0
$87$		−	5.62207e10i		−	1.20932i
$88$		0			0
$89$		−	1.60769e10i		−	0.305181i	−0.988290	−	0.152590i	$-0.951238\pi$
$89$		−	1.60769e10i		−	0.305181i	0.988290	−	0.152590i	$-0.0487615\pi$
$90$		0			0
$91$	−3.60024e9	+	3.60024e9i	−0.0604790	+	0.0604790i
$92$		0			0
$93$	−7.67780e9	−	7.67780e9i	−0.114441	−	0.114441i
$94$		0			0
$95$	−4.51809e10			−0.599066
$96$		0			0
$97$	7.16237e9			0.0846862			0.0423431	−	0.999103i	$-0.486518\pi$
$97$	7.16237e9			0.0846862			0.0423431	+	0.999103i	$0.486518\pi$
$98$		0			0
$99$	−1.56458e10	−	1.56458e10i	−0.165351	−	0.165351i
$100$		0			0
$101$	−5.25797e10	+	5.25797e10i	−0.497795	+	0.497795i	−0.910751	−	0.412956i	$-0.864496\pi$
$101$	−5.25797e10	+	5.25797e10i	−0.497795	+	0.497795i	0.412956	+	0.910751i	$0.364496\pi$
$102$		0			0
$103$		−	1.14829e11i		−	0.975995i	−0.872845	−	0.487998i	$-0.837727\pi$
$103$		−	1.14829e11i		−	0.975995i	0.872845	−	0.487998i	$-0.162273\pi$
$104$		0			0
$105$		−	2.69500e11i		−	2.06071i
$106$		0			0
$107$	8.73178e10	−	8.73178e10i	0.601855	−	0.601855i	−0.338949	−	0.940805i	$-0.610072\pi$
$107$	8.73178e10	−	8.73178e10i	0.601855	−	0.601855i	0.940805	+	0.338949i	$0.110072\pi$
$108$		0			0
$109$	1.89356e10	+	1.89356e10i	0.117878	+	0.117878i	0.763585	−	0.645707i	$-0.223437\pi$
$109$	1.89356e10	+	1.89356e10i	0.117878	+	0.117878i	−0.645707	+	0.763585i	$0.723437\pi$
$110$		0			0
$111$	9.99699e10			0.563110
$112$		0			0
$113$	6.12609e10			0.312790			0.156395	−	0.987695i	$-0.450013\pi$
$113$	6.12609e10			0.312790			0.156395	+	0.987695i	$0.450013\pi$
$114$		0			0
$115$	2.47648e11	+	2.47648e11i	1.14814	+	1.14814i
$116$		0			0
$117$	3.70347e9	−	3.70347e9i	0.0156166	−	0.0156166i
$118$		0			0
$119$			7.48702e11i			2.87608i
$120$		0			0
$121$			2.06943e11i			0.725322i
$122$		0			0
$123$	1.00982e11	−	1.00982e11i	0.323419	−	0.323419i
$124$		0			0
$125$	−2.19647e11	−	2.19647e11i	−0.643754	−	0.643754i
$126$		0			0
$127$	4.12612e11			1.10821			0.554104	−	0.832447i	$-0.313061\pi$
$127$	4.12612e11			1.10821			0.554104	+	0.832447i	$0.313061\pi$
$128$		0			0
$129$	3.11461e11			0.767644
$130$		0			0
$131$	2.28952e11	+	2.28952e11i	0.518503	+	0.518503i	0.917118	−	0.398615i	$-0.130509\pi$
$131$	2.28952e11	+	2.28952e11i	0.518503	+	0.518503i	−0.398615	+	0.917118i	$0.630509\pi$
$132$		0			0
$133$	2.19212e11	−	2.19212e11i	0.456751	−	0.456751i
$134$		0			0
$135$			8.98564e11i			1.72470i
$136$		0			0
$137$		−	9.63336e11i		−	1.70535i	−0.522438	−	0.852677i	$-0.674977\pi$
$137$		−	9.63336e11i		−	1.70535i	0.522438	−	0.852677i	$-0.325023\pi$
$138$		0			0
$139$	8.56724e10	−	8.56724e10i	0.140042	−	0.140042i	−0.633610	−	0.773652i	$-0.718428\pi$
$139$	8.56724e10	−	8.56724e10i	0.140042	−	0.140042i	0.773652	+	0.633610i	$0.218428\pi$
$140$		0			0
$141$	−1.40092e11	−	1.40092e11i	−0.211694	−	0.211694i
$142$		0			0
$143$	1.85504e10			0.0259421
$144$		0			0
$145$	2.00995e12			2.60413
$146$		0			0
$147$	8.69637e11	+	8.69637e11i	1.04494	+	1.04494i
$148$		0			0
$149$	9.78483e11	−	9.78483e11i	1.09151	−	1.09151i	0.0961450	−	0.995367i	$-0.469349\pi$
$149$	9.78483e11	−	9.78483e11i	1.09151	−	1.09151i	0.995367	−	0.0961450i	$-0.0306512\pi$
$150$		0			0
$151$		−	5.06918e11i		−	0.525490i	−0.964865	−	0.262745i	$-0.915372\pi$
$151$		−	5.06918e11i		−	0.525490i	0.964865	−	0.262745i	$-0.0846278\pi$
$152$		0			0
$153$		−	7.70168e11i		−	0.742647i
$154$		0			0
$155$	2.74490e11	−	2.74490e11i	0.246435	−	0.246435i
$156$		0			0
$157$	−1.10917e11	−	1.10917e11i	−0.0928003	−	0.0928003i	0.659183	−	0.751983i	$-0.270902\pi$
$157$	−1.10917e11	−	1.10917e11i	−0.0928003	−	0.0928003i	−0.751983	+	0.659183i	$0.770902\pi$
$158$		0			0
$159$	−6.07226e11			−0.473878
$160$		0			0
$161$	−2.40311e12			−1.75078
$162$		0			0
$163$	−2.13500e11	−	2.13500e11i	−0.145334	−	0.145334i	0.630696	−	0.776030i	$-0.282769\pi$
$163$	−2.13500e11	−	2.13500e11i	−0.145334	−	0.145334i	−0.776030	+	0.630696i	$0.782769\pi$
$164$		0			0
$165$	−6.94305e11	+	6.94305e11i	−0.441966	+	0.441966i
$166$		0			0
$167$		−	1.18776e12i		−	0.707601i	−0.935321	−	0.353801i	$-0.884889\pi$
$167$		−	1.18776e12i		−	0.707601i	0.935321	−	0.353801i	$-0.115111\pi$
$168$		0			0
$169$		−	1.78777e12i		−	0.997550i
$170$		0			0
$171$	−2.25497e11	+	2.25497e11i	−0.117940	+	0.117940i
$172$		0			0
$173$	2.35793e12	+	2.35793e12i	1.15685	+	1.15685i	0.985148	+	0.171705i	$0.0549275\pi$
$173$	2.35793e12	+	2.35793e12i	1.15685	+	1.15685i	0.171705	+	0.985148i	$0.445072\pi$
$174$		0			0
$175$	5.88316e12			2.70958
$176$		0			0
$177$	4.89619e11			0.211839
$178$		0			0
$179$	9.13904e11	+	9.13904e11i	0.371714	+	0.371714i	0.868101	−	0.496387i	$-0.165340\pi$
$179$	9.13904e11	+	9.13904e11i	0.371714	+	0.371714i	−0.496387	+	0.868101i	$0.665340\pi$
$180$		0			0
$181$	2.20066e12	−	2.20066e12i	0.842016	−	0.842016i	−0.147104	−	0.989121i	$-0.546995\pi$
$181$	2.20066e12	−	2.20066e12i	0.842016	−	0.842016i	0.989121	+	0.147104i	$0.0469954\pi$
$182$		0			0
$183$			1.39178e12i			0.501291i
$184$		0			0
$185$			3.57404e12i			1.21259i
$186$		0			0
$187$	1.92886e12	−	1.92886e12i	0.616839	−	0.616839i
$188$		0			0
$189$	−4.35971e12	−	4.35971e12i	−1.31498	−	1.31498i
$190$		0			0
$191$	−4.16073e12			−1.18437			−0.592183	−	0.805804i	$-0.701734\pi$
$191$	−4.16073e12			−1.18437			−0.592183	+	0.805804i	$0.701734\pi$
$192$		0			0
$193$	2.38918e12			0.642220			0.321110	−	0.947042i	$-0.395944\pi$
$193$	2.38918e12			0.642220			0.321110	+	0.947042i	$0.395944\pi$
$194$		0			0
$195$	−1.64346e11	−	1.64346e11i	−0.0417417	−	0.0417417i
$196$		0			0
$197$	3.41311e12	−	3.41311e12i	0.819569	−	0.819569i	−0.166476	−	0.986045i	$-0.553239\pi$
$197$	3.41311e12	−	3.41311e12i	0.819569	−	0.819569i	0.986045	+	0.166476i	$0.0532389\pi$
$198$		0			0
$199$		−	5.08486e12i		−	1.15501i	−0.816386	−	0.577507i	$-0.804026\pi$
$199$		−	5.08486e12i		−	1.15501i	0.816386	−	0.577507i	$-0.195974\pi$
$200$		0			0
$201$		−	1.42578e12i		−	0.306532i
$202$		0			0
$203$	−9.75203e12	+	9.75203e12i	−1.98549	+	1.98549i
$204$		0			0
$205$	3.61021e12	+	3.61021e12i	0.696444	+	0.696444i
$206$		0			0
$207$	2.47201e12			0.452078
$208$		0			0
$209$	−1.12950e12			−0.195921
$210$		0			0
$211$	1.13531e12	+	1.13531e12i	0.186880	+	0.186880i	0.794346	−	0.607466i	$-0.207814\pi$
$211$	1.13531e12	+	1.13531e12i	0.186880	+	0.186880i	−0.607466	+	0.794346i	$0.707814\pi$
$212$		0			0
$213$	3.81410e12	−	3.81410e12i	0.596079	−	0.596079i
$214$		0			0
$215$			1.11351e13i			1.65303i
$216$		0			0
$217$			2.66358e12i			0.375782i
$218$		0			0
$219$	3.39165e12	−	3.39165e12i	0.454955	−	0.454955i
$220$		0			0
$221$	4.56573e11	+	4.56573e11i	0.0582576	+	0.0582576i
$222$		0			0
$223$	4.96676e12			0.603110			0.301555	−	0.953449i	$-0.402494\pi$
$223$	4.96676e12			0.603110			0.301555	+	0.953449i	$0.402494\pi$
$224$		0			0
$225$	−6.05184e12			−0.699654
$226$		0			0
$227$	−9.95306e12	−	9.95306e12i	−1.09601	−	1.09601i	−0.994873	−	0.101137i	$-0.967752\pi$
$227$	−9.95306e12	−	9.95306e12i	−1.09601	−	1.09601i	−0.101137	−	0.994873i	$-0.532248\pi$
$228$		0			0
$229$	−1.28407e13	+	1.28407e13i	−1.34739	+	1.34739i	−0.458896	+	0.888490i	$0.651755\pi$
$229$	−1.28407e13	+	1.28407e13i	−1.34739	+	1.34739i	−0.888490	+	0.458896i	$0.848245\pi$
$230$		0			0
$231$		−	6.73735e12i		−	0.673943i
$232$		0			0
$233$			1.48141e13i			1.41325i	0.707590	+	0.706624i	$0.249783\pi$
$233$			1.48141e13i			1.41325i	−0.707590	+	0.706624i	$0.750217\pi$
$234$		0			0
$235$	5.00844e12	−	5.00844e12i	0.455858	−	0.455858i
$236$		0			0
$237$	−9.85344e12	−	9.85344e12i	−0.855997	−	0.855997i
$238$		0			0
$239$	−1.49728e13			−1.24198			−0.620991	−	0.783818i	$-0.713270\pi$
$239$	−1.49728e13			−1.24198			−0.620991	+	0.783818i	$0.713270\pi$
$240$		0			0
$241$	−1.47290e13			−1.16703			−0.583513	−	0.812104i	$-0.698322\pi$
$241$	−1.47290e13			−1.16703			−0.583513	+	0.812104i	$0.698322\pi$
$242$		0			0
$243$	7.58579e12	+	7.58579e12i	0.574336	+	0.574336i
$244$		0			0
$245$	−3.10905e13	+	3.10905e13i	−2.25016	+	2.25016i
$246$		0			0
$247$		−	2.67359e11i		−	0.0185038i
$248$		0			0
$249$		−	7.15654e12i		−	0.473813i
$250$		0			0
$251$	9.46342e12	−	9.46342e12i	0.599574	−	0.599574i	−0.340625	−	0.940199i	$-0.610639\pi$
$251$	9.46342e12	−	9.46342e12i	0.599574	−	0.599574i	0.940199	+	0.340625i	$0.110639\pi$
$252$		0			0
$253$	6.19106e12	+	6.19106e12i	0.375493	+	0.375493i
$254$		0			0
$255$	−3.41772e13			−1.98502
$256$		0			0
$257$	5.66495e12			0.315184			0.157592	−	0.987504i	$-0.449627\pi$
$257$	5.66495e12			0.315184			0.157592	+	0.987504i	$0.449627\pi$
$258$		0			0
$259$	−1.73407e13	−	1.73407e13i	−0.924526	−	0.924526i
$260$		0			0
$261$	1.00316e13	−	1.00316e13i	0.512683	−	0.512683i
$262$		0			0
$263$		−	3.10458e13i		−	1.52141i	−0.649097	−	0.760706i	$-0.724853\pi$
$263$		−	3.10458e13i		−	1.52141i	0.649097	−	0.760706i	$-0.275147\pi$
$264$		0			0
$265$		−	2.17090e13i		−	1.02044i
$266$		0			0
$267$	−3.56073e12	+	3.56073e12i	−0.160593	+	0.160593i
$268$		0			0
$269$	2.02024e13	+	2.02024e13i	0.874511	+	0.874511i	0.992960	−	0.118449i	$-0.0377924\pi$
$269$	2.02024e13	+	2.02024e13i	0.874511	+	0.874511i	−0.118449	+	0.992960i	$0.537792\pi$
$270$		0			0
$271$	5.30222e12			0.220357			0.110179	−	0.993912i	$-0.464858\pi$
$271$	5.30222e12			0.220357			0.110179	+	0.993912i	$0.464858\pi$
$272$		0			0
$273$	1.59477e12			0.0636509
$274$		0			0
$275$	−1.51566e13	−	1.51566e13i	−0.581129	−	0.581129i
$276$		0			0
$277$	−6.60723e12	+	6.60723e12i	−0.243434	+	0.243434i	−0.818269	−	0.574835i	$-0.805066\pi$
$277$	−6.60723e12	+	6.60723e12i	−0.243434	+	0.243434i	0.574835	+	0.818269i	$0.305066\pi$
$278$		0			0
$279$		−	2.73994e12i		−	0.0970328i
$280$		0			0
$281$			3.22319e13i			1.09749i	0.835990	+	0.548745i	$0.184894\pi$
$281$			3.22319e13i			1.09749i	−0.835990	+	0.548745i	$0.815106\pi$
$282$		0			0
$283$	−9.31687e12	+	9.31687e12i	−0.305102	+	0.305102i	−0.843006	−	0.537904i	$-0.819216\pi$
$283$	−9.31687e12	+	9.31687e12i	−0.305102	+	0.305102i	0.537904	+	0.843006i	$0.319216\pi$
$284$		0			0
$285$	1.00067e13	+	1.00067e13i	0.315243	+	0.315243i
$286$		0			0
$287$	−3.50325e13			−1.06199
$288$		0			0
$289$	6.06763e13			1.77044
$290$		0			0
$291$	−1.58633e12	−	1.58633e12i	−0.0445638	−	0.0445638i
$292$		0			0
$293$	1.68183e13	−	1.68183e13i	0.454999	−	0.454999i	−0.442010	−	0.897010i	$-0.645735\pi$
$293$	1.68183e13	−	1.68183e13i	0.454999	−	0.454999i	0.897010	+	0.442010i	$0.145735\pi$
$294$		0			0
$295$			1.75044e13i			0.456170i
$296$		0			0
$297$			2.24636e13i			0.564052i
$298$		0			0
$299$	−1.46546e12	+	1.46546e12i	−0.0354636	+	0.0354636i
$300$		0			0
$301$	−5.40259e13	−	5.40259e13i	−1.26034	−	1.26034i
$302$		0			0
$303$	2.32909e13			0.523903
$304$		0			0
$305$	−4.97577e13			−1.07947
$306$		0			0
$307$	7.64934e12	+	7.64934e12i	0.160089	+	0.160089i	0.782606	−	0.622517i	$-0.213890\pi$
$307$	7.64934e12	+	7.64934e12i	0.160089	+	0.160089i	−0.622517	+	0.782606i	$0.713890\pi$
$308$		0			0
$309$	−2.54325e13	+	2.54325e13i	−0.513591	+	0.513591i
$310$		0			0
$311$			4.12580e13i			0.804129i	0.915611	+	0.402065i	$0.131707\pi$
$311$			4.12580e13i			0.804129i	−0.915611	+	0.402065i	$0.868293\pi$
$312$		0			0
$313$			1.92404e13i			0.362009i	0.983482	+	0.181004i	$0.0579348\pi$
$313$			1.92404e13i			0.362009i	−0.983482	+	0.181004i	$0.942065\pi$
$314$		0			0
$315$	4.80877e13	−	4.80877e13i	0.873626	−	0.873626i
$316$		0			0
$317$	2.64067e13	+	2.64067e13i	0.463327	+	0.463327i	0.899744	−	0.436417i	$-0.143753\pi$
$317$	2.64067e13	+	2.64067e13i	0.463327	+	0.463327i	−0.436417	+	0.899744i	$0.643753\pi$
$318$		0			0
$319$	5.02477e13			0.851663
$320$		0			0
$321$	−3.86785e13			−0.633420
$322$		0			0
$323$	−2.77998e13	−	2.77998e13i	−0.439975	−	0.439975i
$324$		0			0
$325$	3.58766e12	−	3.58766e12i	0.0548850	−	0.0548850i
$326$		0			0
$327$		−	8.38777e12i		−	0.124061i
$328$		0			0
$329$			4.86006e13i			0.695127i
$330$		0			0
$331$	−7.13929e13	+	7.13929e13i	−0.987645	+	0.987645i	−0.999925	−	0.0122794i	$-0.996091\pi$
$331$	−7.13929e13	+	7.13929e13i	−0.987645	+	0.987645i	0.0122794	+	0.999925i	$0.496091\pi$
$332$		0			0
$333$	1.78379e13	+	1.78379e13i	0.238727	+	0.238727i
$334$		0			0
$335$	5.09734e13			0.660080
$336$		0			0
$337$	−1.21387e14			−1.52128			−0.760640	−	0.649174i	$-0.775115\pi$
$337$	−1.21387e14			−1.52128			−0.760640	+	0.649174i	$0.775115\pi$
$338$		0			0
$339$	−1.35681e13	−	1.35681e13i	−0.164597	−	0.164597i
$340$		0			0
$341$	6.86209e12	−	6.86209e12i	0.0805949	−	0.0805949i
$342$		0			0
$343$		−	1.49764e14i		−	1.70329i
$344$		0			0
$345$		−	1.09699e14i		−	1.20836i
$346$		0			0
$347$	−7.47878e13	+	7.47878e13i	−0.798029	+	0.798029i	−0.982784	−	0.184756i	$-0.940851\pi$
$347$	−7.47878e13	+	7.47878e13i	−0.798029	+	0.798029i	0.184756	+	0.982784i	$0.440851\pi$
$348$		0			0
$349$	−8.65476e13	−	8.65476e13i	−0.894778	−	0.894778i	0.100190	−	0.994968i	$-0.468055\pi$
$349$	−8.65476e13	−	8.65476e13i	−0.894778	−	0.894778i	−0.994968	+	0.100190i	$0.968055\pi$
$350$		0			0
$351$	−5.31728e12			−0.0532721
$352$		0			0
$353$	6.93898e13			0.673806			0.336903	−	0.941539i	$-0.390621\pi$
$353$	6.93898e13			0.673806			0.336903	+	0.941539i	$0.390621\pi$
$354$		0			0
$355$	1.36358e14	+	1.36358e14i	1.28359	+	1.28359i
$356$		0			0
$357$	1.65823e14	−	1.65823e14i	1.51346	−	1.51346i
$358$		0			0
$359$			4.38782e13i			0.388355i	0.980966	+	0.194177i	$0.0622038\pi$
$359$			4.38782e13i			0.388355i	−0.980966	+	0.194177i	$0.937796\pi$
$360$		0			0
$361$		−	1.00211e14i		−	0.860255i
$362$		0			0
$363$	4.58339e13	−	4.58339e13i	0.381681	−	0.381681i
$364$		0			0
$365$	1.21255e14	+	1.21255e14i	0.979692	+	0.979692i
$366$		0			0
$367$	−3.72992e13			−0.292440			−0.146220	−	0.989252i	$-0.546711\pi$
$367$	−3.72992e13			−0.292440			−0.146220	+	0.989252i	$0.546711\pi$
$368$		0			0
$369$	3.60370e13			0.274223
$370$		0			0
$371$	1.05329e14	+	1.05329e14i	0.778023	+	0.778023i
$372$		0			0
$373$	−1.64745e12	+	1.64745e12i	−0.0118144	+	0.0118144i	−0.712989	−	0.701175i	$-0.752659\pi$
$373$	−1.64745e12	+	1.64745e12i	−0.0118144	+	0.0118144i	0.701175	+	0.712989i	$0.252659\pi$
$374$		0			0
$375$			9.72953e13i			0.677517i
$376$		0			0
$377$			1.18940e13i			0.0804357i
$378$		0			0
$379$	−9.18784e13	+	9.18784e13i	−0.603529	+	0.603529i	−0.941247	−	0.337718i	$-0.890345\pi$
$379$	−9.18784e13	+	9.18784e13i	−0.603529	+	0.603529i	0.337718	+	0.941247i	$0.390345\pi$
$380$		0			0
$381$	−9.13858e13	−	9.13858e13i	−0.583165	−	0.583165i
$382$		0			0
$383$	2.80515e14			1.73925			0.869627	−	0.493709i	$-0.164359\pi$
$383$	2.80515e14			1.73925			0.869627	+	0.493709i	$0.164359\pi$
$384$		0			0
$385$	2.40868e14			1.45126
$386$		0			0
$387$	5.55749e13	+	5.55749e13i	0.325438	+	0.325438i
$388$		0			0
$389$	4.93119e13	−	4.93119e13i	0.280691	−	0.280691i	−0.552693	−	0.833385i	$-0.686400\pi$
$389$	4.93119e13	−	4.93119e13i	0.280691	−	0.280691i	0.833385	+	0.552693i	$0.186400\pi$
$390$		0			0
$391$			3.04756e14i			1.68647i
$392$		0			0
$393$		−	1.01417e14i		−	0.545697i
$394$		0			0
$395$	3.52271e14	−	3.52271e14i	1.84329	−	1.84329i
$396$		0			0
$397$	1.03749e14	+	1.03749e14i	0.528001	+	0.528001i	0.919976	−	0.391975i	$-0.128208\pi$
$397$	1.03749e14	+	1.03749e14i	0.528001	+	0.528001i	−0.391975	+	0.919976i	$0.628208\pi$
$398$		0			0
$399$	−9.71026e13			−0.480706
$400$		0			0
$401$	1.70773e14			0.822481			0.411241	−	0.911527i	$-0.365096\pi$
$401$	1.70773e14			0.822481			0.411241	+	0.911527i	$0.365096\pi$
$402$		0			0
$403$	1.62430e12	+	1.62430e12i	0.00761182	+	0.00761182i
$404$		0			0
$405$	8.81480e13	−	8.81480e13i	0.401985	−	0.401985i
$406$		0			0
$407$			8.93489e13i			0.396570i
$408$		0			0
$409$			1.45021e14i			0.626544i	0.949664	+	0.313272i	$0.101425\pi$
$409$			1.45021e14i			0.626544i	−0.949664	+	0.313272i	$0.898575\pi$
$410$		0			0
$411$	−2.13361e14	+	2.13361e14i	−0.897397	+	0.897397i
$412$		0			0
$413$	−8.49291e13	−	8.49291e13i	−0.347801	−	0.347801i
$414$		0			0
$415$	2.55854e14			1.02030
$416$		0			0
$417$	−3.79496e13			−0.147387
$418$		0			0
$419$	3.03198e13	+	3.03198e13i	0.114696	+	0.114696i	0.762126	−	0.647429i	$-0.224156\pi$
$419$	3.03198e13	+	3.03198e13i	0.114696	+	0.114696i	−0.647429	+	0.762126i	$0.724156\pi$
$420$		0			0
$421$	−1.85927e14	+	1.85927e14i	−0.685159	+	0.685159i	−0.961158	−	0.275999i	$-0.910991\pi$
$421$	−1.85927e14	+	1.85927e14i	−0.685159	+	0.685159i	0.275999	+	0.961158i	$0.410991\pi$
$422$		0			0
$423$		−	4.99940e13i		−	0.179492i
$424$		0			0
$425$		−	7.46086e14i		−	2.61005i
$426$		0			0
$427$	2.41418e14	−	2.41418e14i	0.823030	−	0.823030i
$428$		0			0
$429$	−4.10857e12	−	4.10857e12i	−0.0136513	−	0.0136513i
$430$		0			0
$431$	−3.76849e14			−1.22051			−0.610257	−	0.792204i	$-0.708934\pi$
$431$	−3.76849e14			−1.22051			−0.610257	+	0.792204i	$0.708934\pi$
$432$		0			0
$433$	4.33418e14			1.36843			0.684217	−	0.729279i	$-0.260144\pi$
$433$	4.33418e14			1.36843			0.684217	+	0.729279i	$0.260144\pi$
$434$		0			0
$435$	−4.45167e14	−	4.45167e14i	−1.37035	−	1.37035i
$436$		0			0
$437$	8.92291e13	−	8.92291e13i	0.267830	−	0.267830i
$438$		0			0
$439$		−	3.58435e14i		−	1.04919i	−0.851351	−	0.524597i	$-0.824216\pi$
$439$		−	3.58435e14i		−	1.04919i	0.851351	−	0.524597i	$-0.175784\pi$
$440$		0			0
$441$			3.10344e14i			0.885995i
$442$		0			0
$443$	4.66000e14	−	4.66000e14i	1.29767	−	1.29767i	0.367749	−	0.929925i	$-0.380129\pi$
$443$	4.66000e14	−	4.66000e14i	1.29767	−	1.29767i	0.929925	−	0.367749i	$-0.119871\pi$
$444$		0			0
$445$	−1.27300e14	−	1.27300e14i	−0.345819	−	0.345819i
$446$		0			0
$447$	−4.33431e14			−1.14876
$448$		0			0
$449$	−5.16408e14			−1.33548			−0.667741	−	0.744394i	$-0.732739\pi$
$449$	−5.16408e14			−1.33548			−0.667741	+	0.744394i	$0.732739\pi$
$450$		0			0
$451$	9.02533e13	+	9.02533e13i	0.227768	+	0.227768i
$452$		0			0
$453$	−1.12273e14	+	1.12273e14i	−0.276525	+	0.276525i
$454$		0			0
$455$			5.70149e13i			0.137065i
$456$		0			0
$457$			2.08085e14i			0.488316i	0.969735	+	0.244158i	$0.0785115\pi$
$457$			2.08085e14i			0.488316i	−0.969735	+	0.244158i	$0.921488\pi$
$458$		0			0
$459$	−5.52887e14	+	5.52887e14i	−1.26668	+	1.26668i
$460$		0			0
$461$	−1.82664e14	−	1.82664e14i	−0.408599	−	0.408599i	0.472651	−	0.881250i	$-0.343297\pi$
$461$	−1.82664e14	−	1.82664e14i	−0.408599	−	0.408599i	−0.881250	+	0.472651i	$0.843297\pi$
$462$		0			0
$463$	1.40941e13			0.0307851			0.0153926	−	0.999882i	$-0.495100\pi$
$463$	1.40941e13			0.0307851			0.0153926	+	0.999882i	$0.495100\pi$
$464$		0			0
$465$	−1.21589e14			−0.259359
$466$		0			0
$467$	3.52064e14	+	3.52064e14i	0.733465	+	0.733465i	0.971304	−	0.237840i	$-0.0764393\pi$
$467$	3.52064e14	+	3.52064e14i	0.733465	+	0.733465i	−0.237840	+	0.971304i	$0.576439\pi$
$468$		0			0
$469$	−2.47316e14	+	2.47316e14i	−0.503271	+	0.503271i
$470$		0			0
$471$			4.91320e13i			0.0976673i
$472$		0			0
$473$			2.78371e14i			0.540614i
$474$		0			0
$475$	−2.18446e14	+	2.18446e14i	−0.414504	+	0.414504i
$476$		0			0
$477$	−1.08349e14	−	1.08349e14i	−0.200897	−	0.200897i
$478$		0			0
$479$	9.95852e14			1.80447			0.902235	−	0.431246i	$-0.141926\pi$
$479$	9.95852e14			1.80447			0.902235	+	0.431246i	$0.141926\pi$
$480$		0			0
$481$	−2.11495e13			−0.0374543
$482$		0			0
$483$	5.32244e14	+	5.32244e14i	0.921300	+	0.921300i
$484$		0			0
$485$	5.67131e13	−	5.67131e13i	0.0959630	−	0.0959630i
$486$		0			0
$487$			2.25030e14i			0.372247i	0.982526	+	0.186123i	$0.0595924\pi$
$487$			2.25030e14i			0.372247i	−0.982526	+	0.186123i	$0.940408\pi$
$488$		0			0
$489$			9.45727e13i			0.152956i
$490$		0			0
$491$	−4.23772e14	+	4.23772e14i	−0.670168	+	0.670168i	−0.957755	−	0.287586i	$-0.907147\pi$
$491$	−4.23772e14	+	4.23772e14i	−0.670168	+	0.670168i	0.287586	+	0.957755i	$0.407147\pi$
$492$		0			0
$493$	1.23672e15	+	1.23672e15i	1.91256	+	1.91256i
$494$		0			0
$495$	−2.47774e14			−0.374737
$496$		0			0
$497$	−1.32318e15			−1.95731
$498$		0			0
$499$	−5.32410e14	−	5.32410e14i	−0.770359	−	0.770359i	0.207810	−	0.978169i	$-0.433366\pi$
$499$	−5.32410e14	−	5.32410e14i	−0.770359	−	0.770359i	−0.978169	+	0.207810i	$0.933366\pi$
$500$		0			0
$501$	−2.63067e14	+	2.63067e14i	−0.372356	+	0.372356i
$502$		0			0
$503$			1.50984e14i			0.209077i	0.994521	+	0.104538i	$0.0333365\pi$
$503$			1.50984e14i			0.209077i	−0.994521	+	0.104538i	$0.966663\pi$
$504$		0			0
$505$			8.32674e14i			1.12816i
$506$		0			0
$507$	−3.95957e14	+	3.95957e14i	−0.524934	+	0.524934i
$508$		0			0
$509$	3.18716e14	+	3.18716e14i	0.413481	+	0.413481i	0.882949	−	0.469468i	$-0.155554\pi$
$509$	3.18716e14	+	3.18716e14i	0.413481	+	0.413481i	−0.469468	+	0.882949i	$0.655554\pi$
$510$		0			0
$511$	−1.17663e15			−1.49391
$512$		0			0
$513$	3.23758e14			0.402323
$514$		0			0
$515$	−9.09241e14	−	9.09241e14i	−1.10596	−	1.10596i
$516$		0			0
$517$	1.25208e14	−	1.25208e14i	0.149085	−	0.149085i
$518$		0			0
$519$		−	1.04448e15i		−	1.21753i
$520$		0			0
$521$		−	3.32362e14i		−	0.379318i	−0.981850	−	0.189659i	$-0.939262\pi$
$521$		−	3.32362e14i		−	0.379318i	0.981850	−	0.189659i	$-0.0607382\pi$
$522$		0			0
$523$	6.65761e14	−	6.65761e14i	0.743976	−	0.743976i	−0.229364	−	0.973341i	$-0.573665\pi$
$523$	6.65761e14	−	6.65761e14i	0.743976	−	0.743976i	0.973341	+	0.229364i	$0.0736648\pi$
$524$		0			0
$525$	−1.30301e15	−	1.30301e15i	−1.42584	−	1.42584i
$526$		0			0
$527$	3.37787e14			0.361980
$528$		0			0
$529$	−2.53644e13			−0.0266207
$530$		0			0
$531$	8.73641e13	+	8.73641e13i	0.0898076	+	0.0898076i
$532$		0			0
$533$	−2.13635e13	+	2.13635e13i	−0.0215116	+	0.0215116i
$534$		0			0
$535$		−	1.38280e15i		−	1.36400i
$536$		0			0
$537$		−	4.04825e14i		−	0.391209i
$538$		0			0
$539$	−7.77246e14	+	7.77246e14i	−0.735902	+	0.735902i
$540$		0			0
$541$	−5.33393e14	−	5.33393e14i	−0.494837	−	0.494837i	0.414989	−	0.909826i	$-0.363785\pi$
$541$	−5.33393e14	−	5.33393e14i	−0.494837	−	0.494837i	−0.909826	+	0.414989i	$0.863785\pi$
$542$		0			0
$543$	−9.74809e14			−0.886177
$544$		0			0
$545$	2.99872e14			0.267150
$546$		0			0
$547$	−1.27668e15	−	1.27668e15i	−1.11468	−	1.11468i	−0.992509	−	0.122173i	$-0.961014\pi$
$547$	−1.27668e15	−	1.27668e15i	−1.11468	−	1.11468i	−0.122173	−	0.992509i	$-0.538986\pi$
$548$		0			0
$549$	−2.48339e14	+	2.48339e14i	−0.212519	+	0.212519i
$550$		0			0
$551$		−	7.24199e14i		−	0.607469i
$552$		0			0
$553$			3.41835e15i			2.81079i
$554$		0			0
$555$	7.91582e14	−	7.91582e14i	0.638094	−	0.638094i
$556$		0			0
$557$	1.19205e14	+	1.19205e14i	0.0942084	+	0.0942084i	0.752640	−	0.658432i	$-0.228780\pi$
$557$	1.19205e14	+	1.19205e14i	0.0942084	+	0.0942084i	−0.658432	+	0.752640i	$0.728780\pi$
$558$		0			0
$559$	−6.58921e13			−0.0510585
$560$		0			0
$561$	−8.54412e14			−0.649190
$562$		0			0
$563$	−1.83533e15	−	1.83533e15i	−1.36747	−	1.36747i	−0.864025	−	0.503449i	$-0.832064\pi$
$563$	−1.83533e15	−	1.83533e15i	−1.36747	−	1.36747i	−0.503449	−	0.864025i	$-0.667936\pi$
$564$		0			0
$565$	4.85076e14	−	4.85076e14i	0.354441	−	0.354441i
$566$		0			0
$567$			8.55365e14i			0.612978i
$568$		0			0
$569$		−	2.10792e14i		−	0.148162i	−0.997252	−	0.0740810i	$-0.976398\pi$
$569$		−	2.10792e14i		−	0.148162i	0.997252	−	0.0740810i	$-0.0236023\pi$
$570$		0			0
$571$	1.11177e15	−	1.11177e15i	0.766507	−	0.766507i	−0.210983	−	0.977490i	$-0.567666\pi$
$571$	1.11177e15	−	1.11177e15i	0.766507	−	0.766507i	0.977490	+	0.210983i	$0.0676663\pi$
$572$		0			0
$573$	9.21523e14	+	9.21523e14i	0.623241	+	0.623241i
$574$		0			0
$575$	2.39471e15			1.58884
$576$		0			0
$577$	−1.44413e15			−0.940024			−0.470012	−	0.882660i	$-0.655750\pi$
$577$	−1.44413e15			−0.940024			−0.470012	+	0.882660i	$0.655750\pi$
$578$		0			0
$579$	−5.29159e14	−	5.29159e14i	−0.337951	−	0.337951i
$580$		0			0
$581$	−1.24137e15	+	1.24137e15i	−0.777916	+	0.777916i
$582$		0			0
$583$		−	5.42713e14i		−	0.333728i
$584$		0			0
$585$		−	5.86496e13i		−	0.0353922i
$586$		0			0
$587$	−9.87281e14	+	9.87281e14i	−0.584698	+	0.584698i	−0.936191	−	0.351493i	$-0.885674\pi$
$587$	−9.87281e14	+	9.87281e14i	−0.584698	+	0.584698i	0.351493	+	0.936191i	$0.385674\pi$
$588$		0			0
$589$	−9.89004e13	−	9.89004e13i	−0.0574862	−	0.0574862i
$590$		0			0
$591$	−1.51188e15			−0.862553
$592$		0			0
$593$	1.56359e15			0.875632			0.437816	−	0.899065i	$-0.355752\pi$
$593$	1.56359e15			0.875632			0.437816	+	0.899065i	$0.355752\pi$
$594$		0			0
$595$	5.92837e15	+	5.92837e15i	3.25906	+	3.25906i
$596$		0			0
$597$	−1.12620e15	+	1.12620e15i	−0.607795	+	0.607795i
$598$		0			0
$599$			3.21984e15i			1.70603i	0.521886	+	0.853015i	$0.325229\pi$
$599$			3.21984e15i			1.70603i	−0.521886	+	0.853015i	$0.674771\pi$
$600$		0			0
$601$		−	3.71403e15i		−	1.93213i	−0.258303	−	0.966064i	$-0.583163\pi$
$601$		−	3.71403e15i		−	1.93213i	0.258303	−	0.966064i	$-0.416837\pi$
$602$		0			0
$603$	2.54407e14	−	2.54407e14i	0.129952	−	0.129952i
$604$		0			0
$605$	1.63861e15	+	1.63861e15i	0.821906	+	0.821906i
$606$		0			0
$607$	−3.66834e15			−1.80689			−0.903446	−	0.428703i	$-0.858971\pi$
$607$	−3.66834e15			−1.80689			−0.903446	+	0.428703i	$0.858971\pi$
$608$		0			0
$609$	4.31978e15			2.08962
$610$		0			0
$611$	2.96376e13	+	2.96376e13i	0.0140804	+	0.0140804i
$612$		0			0
$613$	1.62841e15	−	1.62841e15i	0.759854	−	0.759854i	−0.216442	−	0.976295i	$-0.569445\pi$
$613$	1.62841e15	−	1.62841e15i	0.759854	−	0.759854i	0.976295	+	0.216442i	$0.0694452\pi$
$614$		0			0
$615$		−	1.59919e15i		−	0.732970i
$616$		0			0
$617$		−	2.70508e15i		−	1.21790i	−0.793208	−	0.608950i	$-0.791591\pi$
$617$		−	2.70508e15i		−	1.21790i	0.793208	−	0.608950i	$-0.208409\pi$
$618$		0			0
$619$	−1.12450e15	+	1.12450e15i	−0.497349	+	0.497349i	−0.910612	−	0.413263i	$-0.864389\pi$
$619$	−1.12450e15	+	1.12450e15i	−0.497349	+	0.497349i	0.413263	+	0.910612i	$0.364389\pi$
$620$		0			0
$621$	−1.77460e15	−	1.77460e15i	−0.771075	−	0.771075i
$622$		0			0
$623$	1.23529e15			0.527331
$624$		0			0
$625$	2.60238e14			0.109152
$626$		0			0
$627$	2.50163e14	+	2.50163e14i	0.103098	+	0.103098i
$628$		0			0
$629$	−2.19910e15	+	2.19910e15i	−0.890569	+	0.890569i
$630$		0			0
$631$			3.62826e15i			1.44390i	0.691947	+	0.721949i	$0.256753\pi$
$631$			3.62826e15i			1.44390i	−0.691947	+	0.721949i	$0.743247\pi$
$632$		0			0
$633$		−	5.02901e14i		−	0.196681i
$634$		0			0
$635$	3.26714e15	−	3.26714e15i	1.25578	−	1.25578i
$636$		0			0
$637$	−1.83979e14	−	1.83979e14i	−0.0695026	−	0.0695026i
$638$		0			0
$639$	1.36112e15			0.505408
$640$		0			0
$641$	−2.02765e15			−0.740071			−0.370036	−	0.929018i	$-0.620655\pi$
$641$	−2.02765e15			−0.740071			−0.370036	+	0.929018i	$0.620655\pi$
$642$		0			0
$643$	−1.68717e15	−	1.68717e15i	−0.605340	−	0.605340i	0.336385	−	0.941725i	$-0.390796\pi$
$643$	−1.68717e15	−	1.68717e15i	−0.605340	−	0.605340i	−0.941725	+	0.336385i	$0.890796\pi$
$644$		0			0
$645$	2.46621e15	−	2.46621e15i	0.869864	−	0.869864i
$646$		0			0
$647$			1.10797e15i			0.384197i	0.981376	+	0.192098i	$0.0615293\pi$
$647$			1.10797e15i			0.384197i	−0.981376	+	0.192098i	$0.938471\pi$
$648$		0			0
$649$			4.37601e14i			0.149187i
$650$		0			0
$651$	5.89932e14	−	5.89932e14i	0.197745	−	0.197745i
$652$		0			0
$653$	1.66210e15	+	1.66210e15i	0.547816	+	0.547816i	0.925809	−	0.377993i	$-0.123386\pi$
$653$	1.66210e15	+	1.66210e15i	0.547816	+	0.547816i	−0.377993	+	0.925809i	$0.623386\pi$
$654$		0			0
$655$	3.62577e15			1.17509
$656$		0			0
$657$	1.21036e15			0.385750
$658$		0			0
$659$	−5.89720e14	−	5.89720e14i	−0.184832	−	0.184832i	0.608626	−	0.793457i	$-0.291721\pi$
$659$	−5.89720e14	−	5.89720e14i	−0.184832	−	0.184832i	−0.793457	+	0.608626i	$0.791721\pi$
$660$		0			0
$661$	2.71945e15	−	2.71945e15i	0.838247	−	0.838247i	−0.150381	−	0.988628i	$-0.548050\pi$
$661$	2.71945e15	−	2.71945e15i	0.838247	−	0.838247i	0.988628	+	0.150381i	$0.0480499\pi$
$662$		0			0
$663$		−	2.02245e14i		−	0.0613130i
$664$		0			0
$665$		−	3.47152e15i		−	1.03514i
$666$		0			0
$667$	−3.96952e15	+	3.96952e15i	−1.16425	+	1.16425i
$668$		0			0
$669$	−1.10004e15	−	1.10004e15i	−0.317370	−	0.317370i
$670$		0			0
$671$	−1.24391e15			−0.353034
$672$		0			0
$673$	−2.23065e15			−0.622801			−0.311400	−	0.950279i	$-0.600798\pi$
$673$	−2.23065e15			−0.622801			−0.311400	+	0.950279i	$0.600798\pi$
$674$		0			0
$675$	4.34448e15	+	4.34448e15i	1.19335	+	1.19335i
$676$		0			0
$677$	−3.84026e14	+	3.84026e14i	−0.103782	+	0.103782i	−0.757091	−	0.653309i	$-0.773380\pi$
$677$	−3.84026e14	+	3.84026e14i	−0.103782	+	0.103782i	0.653309	+	0.757091i	$0.273380\pi$
$678$		0			0
$679$			5.50329e14i			0.146332i
$680$		0			0
$681$			4.40883e15i			1.15349i
$682$		0			0
$683$	5.42054e14	−	5.42054e14i	0.139550	−	0.139550i	−0.633881	−	0.773431i	$-0.718539\pi$
$683$	5.42054e14	−	5.42054e14i	0.139550	−	0.139550i	0.773431	+	0.633881i	$0.218539\pi$
$684$		0			0
$685$	−7.62789e15	−	7.62789e15i	−1.93244	−	1.93244i
$686$		0			0
$687$	5.68793e15			1.41805
$688$		0			0
$689$	1.28464e14			0.0315191
$690$		0			0
$691$	1.50768e15	+	1.50768e15i	0.364065	+	0.364065i	0.865307	−	0.501242i	$-0.167123\pi$
$691$	1.50768e15	+	1.50768e15i	0.364065	+	0.364065i	−0.501242	+	0.865307i	$0.667123\pi$
$692$		0			0
$693$	1.20217e15	−	1.20217e15i	0.285714	−	0.285714i
$694$		0			0
$695$		−	1.35674e15i		−	0.317381i
$696$		0			0
$697$			4.44273e15i			1.02298i
$698$		0			0
$699$	3.28105e15	−	3.28105e15i	0.743684	−	0.743684i
$700$		0			0
$701$	2.70192e15	+	2.70192e15i	0.602870	+	0.602870i	0.941073	−	0.338203i	$-0.109819\pi$
$701$	2.70192e15	+	2.70192e15i	0.602870	+	0.602870i	−0.338203	+	0.941073i	$0.609819\pi$
$702$		0			0
$703$	1.28775e15			0.282863
$704$		0			0
$705$	−2.21855e15			−0.479766
$706$		0			0
$707$	−4.04002e15	−	4.04002e15i	−0.860156	−	0.860156i
$708$		0			0
$709$	−2.03058e15	+	2.03058e15i	−0.425663	+	0.425663i	−0.887148	−	0.461485i	$-0.847317\pi$
$709$	−2.03058e15	+	2.03058e15i	−0.425663	+	0.425663i	0.461485	+	0.887148i	$0.347317\pi$
$710$		0			0
$711$		−	3.51636e15i		−	0.725789i
$712$		0			0
$713$			1.08420e15i			0.220351i
$714$		0			0
$715$	1.46886e14	−	1.46886e14i	0.0293966	−	0.0293966i
$716$		0			0
$717$	3.31620e15	+	3.31620e15i	0.653560	+	0.653560i
$718$		0			0
$719$	−2.42675e15			−0.470995			−0.235498	−	0.971875i	$-0.575672\pi$
$719$	−2.42675e15			−0.470995			−0.235498	+	0.971875i	$0.575672\pi$
$720$		0			0
$721$	8.82303e15			1.68645
$722$		0			0
$723$	3.26221e15	+	3.26221e15i	0.614117	+	0.614117i
$724$		0			0
$725$	9.71795e15	−	9.71795e15i	1.80184	−	1.80184i
$726$		0			0
$727$			2.47046e15i			0.451168i	0.974224	+	0.225584i	$0.0724290\pi$
$727$			2.47046e15i			0.451168i	−0.974224	+	0.225584i	$0.927571\pi$
$728$		0			0
$729$		−	5.33228e15i		−	0.959205i
$730$		0			0
$731$	−6.85141e15	+	6.85141e15i	−1.21404	+	1.21404i
$732$		0			0
$733$	2.16629e15	+	2.16629e15i	0.378132	+	0.378132i	0.870428	−	0.492296i	$-0.163842\pi$
$733$	2.16629e15	+	2.16629e15i	0.378132	+	0.378132i	−0.492296	+	0.870428i	$0.663842\pi$
$734$		0			0
$735$	1.37719e16			2.36818
$736$		0			0
$737$	1.27431e15			0.215875
$738$		0			0
$739$	1.12857e15	+	1.12857e15i	0.188357	+	0.188357i	0.794986	−	0.606628i	$-0.207478\pi$
$739$	1.12857e15	+	1.12857e15i	0.188357	+	0.188357i	−0.606628	+	0.794986i	$0.707478\pi$
$740$		0			0
$741$	−5.92150e13	+	5.92150e13i	−0.00973715	+	0.00973715i
$742$		0			0
$743$			4.70323e14i			0.0762004i	0.999274	+	0.0381002i	$0.0121306\pi$
$743$			4.70323e14i			0.0762004i	−0.999274	+	0.0381002i	$0.987869\pi$
$744$		0			0
$745$		−	1.54956e16i		−	2.47372i
$746$		0			0
$747$	1.27696e15	−	1.27696e15i	0.200870	−	0.200870i
$748$		0			0
$749$	6.70916e15	+	6.70916e15i	1.03996	+	1.03996i
$750$		0			0
$751$	−1.15370e16			−1.76227			−0.881133	−	0.472868i	$-0.843219\pi$
$751$	−1.15370e16			−1.76227			−0.881133	+	0.472868i	$0.843219\pi$
$752$		0			0
$753$	−4.19194e15			−0.631020
$754$		0			0
$755$	−4.01388e15	−	4.01388e15i	−0.595464	−	0.595464i
$756$		0			0
$757$	6.27731e15	−	6.27731e15i	0.917796	−	0.917796i	−0.0790730	−	0.996869i	$-0.525196\pi$
$757$	6.27731e15	−	6.27731e15i	0.917796	−	0.917796i	0.996869	+	0.0790730i	$0.0251960\pi$
$758$		0			0
$759$		−	2.74241e15i		−	0.395187i
$760$		0			0
$761$			1.00942e16i			1.43370i	0.697229	+	0.716848i	$0.254416\pi$
$761$			1.00942e16i			1.43370i	−0.697229	+	0.716848i	$0.745584\pi$
$762$		0			0
$763$	−1.45494e15	+	1.45494e15i	−0.203685	+	0.203685i
$764$		0			0
$765$	−6.09834e15	−	6.09834e15i	−0.841539	−	0.841539i
$766$		0			0
$767$	−1.03583e14			−0.0140901
$768$		0			0
$769$	−1.23395e15			−0.165463			−0.0827316	−	0.996572i	$-0.526364\pi$
$769$	−1.23395e15			−0.165463			−0.0827316	+	0.996572i	$0.526364\pi$
$770$		0			0
$771$	−1.25468e15	−	1.25468e15i	−0.165857	−	0.165857i
$772$		0			0
$773$	−2.67045e15	+	2.67045e15i	−0.348015	+	0.348015i	−0.859370	−	0.511355i	$-0.829144\pi$
$773$	−2.67045e15	+	2.67045e15i	−0.348015	+	0.348015i	0.511355	+	0.859370i	$0.329144\pi$
$774$		0			0
$775$		−	2.65427e15i		−	0.341024i
$776$		0			0
$777$			7.68130e15i			0.973014i
$778$		0			0
$779$	1.30078e15	−	1.30078e15i	0.162461	−	0.162461i
$780$		0			0
$781$	3.40888e15	+	3.40888e15i	0.419789	+	0.419789i
$782$		0			0
$783$	−1.44030e16			−1.74889
$784$		0			0
$785$	−1.75652e15			−0.210315
$786$		0			0
$787$	6.44867e14	+	6.44867e14i	0.0761394	+	0.0761394i	0.744151	−	0.668012i	$-0.232854\pi$
$787$	6.44867e14	+	6.44867e14i	0.0761394	+	0.0761394i	−0.668012	+	0.744151i	$0.732854\pi$
$788$		0			0
$789$	−6.87607e15	+	6.87607e15i	−0.800602	+	0.800602i
$790$		0			0
$791$			4.70705e15i			0.540478i
$792$		0			0
$793$		−	2.94442e14i		−	0.0333425i
$794$		0			0
$795$	−4.80814e15	+	4.80814e15i	−0.536979	+	0.536979i
$796$		0			0
$797$	−5.49268e15	−	5.49268e15i	−0.605011	−	0.605011i	0.336627	−	0.941638i	$-0.390714\pi$
$797$	−5.49268e15	−	5.49268e15i	−0.605011	−	0.605011i	−0.941638	+	0.336627i	$0.890714\pi$
$798$		0			0
$799$	6.16339e15			0.669595
$800$		0			0
$801$	−1.27070e15			−0.136165
$802$		0			0
$803$	3.03131e15	+	3.03131e15i	0.320402	+	0.320402i
$804$		0			0
$805$	−1.90283e16	+	1.90283e16i	−1.98391	+	1.98391i
$806$		0			0
$807$		−	8.94890e15i		−	0.920376i
$808$		0			0
$809$			6.25279e14i			0.0634391i	0.999497	+	0.0317196i	$0.0100983\pi$
$809$			6.25279e14i			0.0634391i	−0.999497	+	0.0317196i	$0.989902\pi$
$810$		0			0
$811$	1.11110e16	−	1.11110e16i	1.11209	−	1.11209i	0.119217	−	0.992868i	$-0.461962\pi$
$811$	1.11110e16	−	1.11110e16i	1.11209	−	1.11209i	0.992868	−	0.119217i	$-0.0380383\pi$
$812$		0			0
$813$	−1.17434e15	−	1.17434e15i	−0.115957	−	0.115957i
$814$		0			0
$815$	−3.38108e15			−0.329373
$816$		0			0
$817$	4.01204e15			0.385606
$818$		0			0
$819$	2.84560e14	+	2.84560e14i	0.0269844	+	0.0269844i
$820$		0			0
$821$	−1.02695e16	+	1.02695e16i	−0.960868	+	0.960868i	−0.999263	−	0.0383942i	$-0.987776\pi$
$821$	−1.02695e16	+	1.02695e16i	−0.960868	+	0.960868i	0.0383942	+	0.999263i	$0.487776\pi$
$822$		0			0
$823$			1.28724e15i			0.118839i	0.998233	+	0.0594196i	$0.0189250\pi$
$823$			1.28724e15i			0.118839i	−0.998233	+	0.0594196i	$0.981075\pi$
$824$		0			0
$825$			6.71381e15i			0.611607i
$826$		0			0
$827$	1.67205e15	−	1.67205e15i	0.150303	−	0.150303i	−0.627950	−	0.778254i	$-0.716106\pi$
$827$	1.67205e15	−	1.67205e15i	0.150303	−	0.150303i	0.778254	+	0.627950i	$0.216106\pi$
$828$		0			0
$829$	1.91391e15	+	1.91391e15i	0.169774	+	0.169774i	0.786880	−	0.617106i	$-0.211695\pi$
$829$	1.91391e15	+	1.91391e15i	0.169774	+	0.169774i	−0.617106	+	0.786880i	$0.711695\pi$
$830$		0			0
$831$	2.92675e15			0.256201
$832$		0			0
$833$	−3.82600e16			−3.30520
$834$		0			0
$835$	−9.40493e15	−	9.40493e15i	−0.801825	−	0.801825i
$836$		0			0
$837$	−1.96694e15	+	1.96694e15i	−0.165502	+	0.165502i
$838$		0			0
$839$			2.99466e15i			0.248689i	0.992239	+	0.124344i	$0.0396828\pi$
$839$			2.99466e15i			0.248689i	−0.992239	+	0.124344i	$0.960317\pi$
$840$		0			0
$841$			2.00168e16i			1.64065i
$842$		0			0
$843$	7.13875e15	−	7.13875e15i	0.577525	−	0.577525i
$844$		0			0
$845$	−1.41559e16	−	1.41559e16i	−1.13038	−	1.13038i
$846$		0			0
$847$	−1.59007e16			−1.25330
$848$		0			0
$849$	4.12703e15			0.321103
$850$		0			0
$851$	−7.05847e15	−	7.05847e15i	−0.542123	−	0.542123i
$852$		0			0
$853$	−5.11390e15	+	5.11390e15i	−0.387733	+	0.387733i	−0.873878	−	0.486145i	$-0.838403\pi$
$853$	−5.11390e15	+	5.11390e15i	−0.387733	+	0.387733i	0.486145	+	0.873878i	$0.338403\pi$
$854$		0			0
$855$			3.57106e15i			0.267290i
$856$		0			0
$857$		−	2.39090e16i		−	1.76672i	−0.468695	−	0.883360i	$-0.655276\pi$
$857$		−	2.39090e16i		−	1.76672i	0.468695	−	0.883360i	$-0.344724\pi$
$858$		0			0
$859$	−1.89252e16	+	1.89252e16i	−1.38063	+	1.38063i	−0.537135	+	0.843496i	$0.680493\pi$
$859$	−1.89252e16	+	1.89252e16i	−1.38063	+	1.38063i	−0.843496	+	0.537135i	$0.819507\pi$
$860$		0			0
$861$	7.75905e15	+	7.75905e15i	0.558845	+	0.558845i
$862$		0			0
$863$	−1.36780e16			−0.972666			−0.486333	−	0.873774i	$-0.661666\pi$
$863$	−1.36780e16			−0.972666			−0.486333	+	0.873774i	$0.661666\pi$
$864$		0			0
$865$	3.73412e16			2.62180
$866$		0			0
$867$	−1.34387e16	−	1.34387e16i	−0.931647	−	0.931647i
$868$		0			0
$869$	8.80660e15	−	8.80660e15i	0.602836	−	0.602836i
$870$		0			0
$871$			3.01636e14i			0.0203884i
$872$		0			0
$873$		−	5.66108e14i		−	0.0377851i
$874$		0			0
$875$	1.68768e16	−	1.68768e16i	1.11236	−	1.11236i
$876$		0			0
$877$	7.71502e15	+	7.71502e15i	0.502157	+	0.502157i	0.912108	−	0.409951i	$-0.134454\pi$
$877$	7.71502e15	+	7.71502e15i	0.502157	+	0.502157i	−0.409951	+	0.912108i	$0.634454\pi$
$878$		0			0
$879$	−7.44989e15			−0.478863
$880$		0			0
$881$	1.75193e14			0.0111211			0.00556056	−	0.999985i	$-0.498230\pi$
$881$	1.75193e14			0.0111211			0.00556056	+	0.999985i	$0.498230\pi$
$882$		0			0
$883$	−6.13677e15	−	6.13677e15i	−0.384730	−	0.384730i	0.488073	−	0.872803i	$-0.337700\pi$
$883$	−6.13677e15	−	6.13677e15i	−0.384730	−	0.384730i	−0.872803	+	0.488073i	$0.837700\pi$
$884$		0			0
$885$	3.87690e15	−	3.87690e15i	0.240047	−	0.240047i
$886$		0			0
$887$			1.65882e15i			0.101442i	0.998713	+	0.0507211i	$0.0161520\pi$
$887$			1.65882e15i			0.101442i	−0.998713	+	0.0507211i	$0.983848\pi$
$888$		0			0
$889$			3.17035e16i			1.91491i
$890$		0			0
$891$	2.20365e15	−	2.20365e15i	0.131467	−	0.131467i
$892$		0			0
$893$	−1.80457e15	−	1.80457e15i	−0.106339	−	0.106339i
$894$		0			0
$895$	1.44729e16			0.842423
$896$		0			0
$897$	6.49145e14			0.0373236
$898$		0			0
$899$	4.39976e15	+	4.39976e15i	0.249891	+	0.249891i
$900$		0			0
$901$	1.33575e16	−	1.33575e16i	0.749446	−	0.749446i
$902$		0			0
$903$			2.39314e16i			1.32644i
$904$		0			0
$905$		−	3.48505e16i		−	1.90828i
$906$		0			0
$907$	−1.46370e16	+	1.46370e16i	−0.791796	+	0.791796i	−0.981786	−	0.189990i	$-0.939154\pi$
$907$	−1.46370e16	+	1.46370e16i	−0.791796	+	0.791796i	0.189990	+	0.981786i	$0.439154\pi$
$908$		0			0
$909$	4.15586e15	+	4.15586e15i	0.222105	+	0.222105i
$910$		0			0
$911$	5.40386e15			0.285333			0.142667	−	0.989771i	$-0.454432\pi$
$911$	5.40386e15			0.285333			0.142667	+	0.989771i	$0.454432\pi$
$912$		0			0
$913$	6.39622e15			0.333683
$914$		0			0
$915$	1.10204e16	+	1.10204e16i	0.568043	+	0.568043i
$916$		0			0
$917$	−1.75917e16	+	1.75917e16i	−0.895937	+	0.895937i
$918$		0			0
$919$		−	3.33548e16i		−	1.67850i	−0.543743	−	0.839252i	$-0.682993\pi$
$919$		−	3.33548e16i		−	1.67850i	0.543743	−	0.839252i	$-0.317007\pi$
$920$		0			0
$921$		−	3.38837e15i		−	0.168486i
$922$		0			0
$923$	−8.06903e14	+	8.06903e14i	−0.0396471	+	0.0396471i
$924$		0			0
$925$	1.72802e16	+	1.72802e16i	0.839012	+	0.839012i
$926$		0			0
$927$	−9.07600e15			−0.435468
$928$		0			0
$929$	1.87508e16			0.889064			0.444532	−	0.895763i	$-0.353370\pi$
$929$	1.87508e16			0.889064			0.444532	+	0.895763i	$0.353370\pi$
$930$		0			0
$931$	1.12021e16	+	1.12021e16i	0.524900	+	0.524900i
$932$		0			0
$933$	9.13787e15	−	9.13787e15i	0.423151	−	0.423151i
$934$		0			0
$935$		−	3.05462e16i		−	1.39795i
$936$		0			0
$937$			2.19543e16i			0.993005i	0.868035	+	0.496502i	$0.165383\pi$
$937$			2.19543e16i			0.993005i	−0.868035	+	0.496502i	$0.834617\pi$
$938$		0			0
$939$	4.26138e15	−	4.26138e15i	0.190498	−	0.190498i
$940$		0			0
$941$	−1.75023e15	−	1.75023e15i	−0.0773309	−	0.0773309i	0.667383	−	0.744714i	$-0.267414\pi$
$941$	−1.75023e15	−	1.75023e15i	−0.0773309	−	0.0773309i	−0.744714	+	0.667383i	$0.767414\pi$
$942$		0			0
$943$	−1.42598e16			−0.622730
$944$		0			0
$945$	−6.90421e16			−2.98016
$946$		0			0
$947$	1.97786e16	+	1.97786e16i	0.843860	+	0.843860i	0.989358	−	0.145498i	$-0.0464786\pi$
$947$	1.97786e16	+	1.97786e16i	0.843860	+	0.843860i	−0.145498	+	0.989358i	$0.546479\pi$
$948$		0			0
$949$	−7.17531e14	+	7.17531e14i	−0.0302605	+	0.0302605i
$950$		0			0
$951$		−	1.16972e16i		−	0.487627i
$952$		0			0
$953$			1.12547e16i			0.463793i	0.972740	+	0.231897i	$0.0744931\pi$
$953$			1.12547e16i			0.463793i	−0.972740	+	0.231897i	$0.925507\pi$
$954$		0			0
$955$	−3.29455e16	+	3.29455e16i	−1.34208	+	1.34208i
$956$		0			0
$957$	−1.11289e16	−	1.11289e16i	−0.448165	−	0.448165i
$958$		0			0
$959$	7.40190e16			2.94673
$960$		0			0
$961$	−2.42068e16			−0.952704
$962$		0			0
$963$	−6.90152e15	−	6.90152e15i	−0.268535	−	0.268535i
$964$		0			0
$965$	1.89180e16	−	1.89180e16i	0.727738	−	0.727738i
$966$		0			0
$967$		−	2.27290e16i		−	0.864441i	−0.901768	−	0.432220i	$-0.857730\pi$
$967$		−	2.27290e16i		−	0.864441i	0.901768	−	0.432220i	$-0.142270\pi$
$968$		0			0
$969$			1.23143e16i			0.463050i
$970$		0			0
$971$	2.10096e16	−	2.10096e16i	0.781110	−	0.781110i	−0.198908	−	0.980018i	$-0.563740\pi$
$971$	2.10096e16	−	2.10096e16i	0.781110	−	0.781110i	0.980018	+	0.198908i	$0.0637395\pi$
$972$		0			0
$973$	6.58273e15	+	6.58273e15i	0.241983	+	0.241983i
$974$		0			0
$975$	−1.58920e15			−0.0577635
$976$		0			0
$977$	1.01681e16			0.365445			0.182722	−	0.983165i	$-0.441509\pi$
$977$	1.01681e16			0.365445			0.182722	+	0.983165i	$0.441509\pi$
$978$		0			0
$979$	−3.18243e15	−	3.18243e15i	−0.113098	−	0.113098i
$980$		0			0
$981$	1.49666e15	−	1.49666e15i	0.0525947	−	0.0525947i
$982$		0			0
$983$			3.52097e16i			1.22354i	0.791035	+	0.611770i	$0.209542\pi$
$983$			3.52097e16i			1.22354i	−0.791035	+	0.611770i	$0.790458\pi$
$984$		0			0
$985$		−	5.40513e16i		−	1.85741i
$986$		0			0
$987$	1.07641e16	−	1.07641e16i	0.365792	−	0.365792i
$988$		0			0
$989$	−2.19910e16	−	2.19910e16i	−0.739035	−	0.739035i
$990$		0			0
$991$	8.14787e15			0.270794			0.135397	−	0.990791i	$-0.456769\pi$
$991$	8.14787e15			0.270794			0.135397	+	0.990791i	$0.456769\pi$
$992$		0			0
$993$	3.16244e16			1.03944
$994$		0			0
$995$	−4.02629e16	−	4.02629e16i	−1.30882	−	1.30882i
$996$		0			0
$997$	2.72862e16	−	2.72862e16i	0.877243	−	0.877243i	−0.116006	−	0.993249i	$-0.537009\pi$
$997$	2.72862e16	−	2.72862e16i	0.877243	−	0.877243i	0.993249	+	0.116006i	$0.0370091\pi$
$998$		0			0
$999$		−	2.56109e16i		−	0.814357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.7		42
4.3	odd	2		128.12.e.a.33.15		42
8.3	odd	2		64.12.e.a.17.7		42
8.5	even	2		16.12.e.a.13.19	yes	42
16.3	odd	4		64.12.e.a.49.7		42
16.5	even	4	inner	128.12.e.b.97.7		42
16.11	odd	4		128.12.e.a.97.15		42
16.13	even	4		16.12.e.a.5.19	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.19	✓	42	16.13	even	4
16.12.e.a.13.19	yes	42	8.5	even	2
64.12.e.a.17.7		42	8.3	odd	2
64.12.e.a.49.7		42	16.3	odd	4
128.12.e.a.33.15		42	4.3	odd	2
128.12.e.a.97.15		42	16.11	odd	4
128.12.e.b.33.7		42	1.1	even	1	trivial
128.12.e.b.97.7		42	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-221.481 - 221.481i) q^{3} +(7918.20 - 7918.20i) q^{5} +76836.1i q^{7} -79039.1i q^{9} +O(q^{10})\)	\(q+(-221.481 - 221.481i) q^{3} +(7918.20 - 7918.20i) q^{5} +76836.1i q^{7} -79039.1i q^{9} +(197951. - 197951. i) q^{11} +(46856.2 + 46856.2i) q^{13} -3.50747e6 q^{15} +9.74414e6 q^{17} +(-2.85298e6 - 2.85298e6i) q^{19} +(1.70178e7 - 1.70178e7i) q^{21} +3.12758e7i q^{23} -7.65676e7i q^{25} +(-5.67404e7 + 5.67404e7i) q^{27} +(1.26920e8 + 1.26920e8i) q^{29} +3.46657e7 q^{31} -8.76847e7 q^{33} +(6.08404e8 + 6.08404e8i) q^{35} +(-2.25685e8 + 2.25685e8i) q^{37} -2.07555e7i q^{39} +4.55938e8i q^{41} +(-7.03132e8 + 7.03132e8i) q^{43} +(-6.25847e8 - 6.25847e8i) q^{45} +6.32523e8 q^{47} -3.92646e9 q^{49} +(-2.15814e9 - 2.15814e9i) q^{51} +(1.37083e9 - 1.37083e9i) q^{53} -3.13483e9i q^{55} +1.26376e9i q^{57} +(-1.10533e9 + 1.10533e9i) q^{59} +(-3.14198e9 - 3.14198e9i) q^{61} +6.07306e9 q^{63} +7.42033e8 q^{65} +(3.21875e9 + 3.21875e9i) q^{67} +(6.92700e9 - 6.92700e9i) q^{69} +1.72208e10i q^{71} +1.53135e10i q^{73} +(-1.69583e10 + 1.69583e10i) q^{75} +(1.52098e10 + 1.52098e10i) q^{77} +4.44888e10 q^{79} +1.11323e10 q^{81} +(1.61561e10 + 1.61561e10i) q^{83} +(7.71560e10 - 7.71560e10i) q^{85} -5.62207e10i q^{87} -1.60769e10i q^{89} +(-3.60024e9 + 3.60024e9i) q^{91} +(-7.67780e9 - 7.67780e9i) q^{93} -4.51809e10 q^{95} +7.16237e9 q^{97} +(-1.56458e10 - 1.56458e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 + 2 * q^5	\( 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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