LMFDB - Embedded newform 17.16.c.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,16,Mod(4,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("17.4");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	17.c (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.2578958670$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	17.4
Dual form			17.16.c.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+274.663i q^{2} +(931.417 - 931.417i) q^{3} -42671.9 q^{4} +(129422. - 129422. i) q^{5} +(255826. + 255826. i) q^{6} +(151712. + 151712. i) q^{7} -2.72024e6i q^{8} +1.26138e7i q^{9} +O(q^{10})$	\(q+274.663i q^{2} +(931.417 - 931.417i) q^{3} -42671.9 q^{4} +(129422. - 129422. i) q^{5} +(255826. + 255826. i) q^{6} +(151712. + 151712. i) q^{7} -2.72024e6i q^{8} +1.26138e7i q^{9} +(3.55476e7 + 3.55476e7i) q^{10} +(-5.86645e7 - 5.86645e7i) q^{11} +(-3.97454e7 + 3.97454e7i) q^{12} -4.27582e8 q^{13} +(-4.16696e7 + 4.16696e7i) q^{14} -2.41092e8i q^{15} -6.51123e8 q^{16} +(4.95538e8 + 1.61767e9i) q^{17} -3.46456e9 q^{18} +4.87297e9i q^{19} +(-5.52270e9 + 5.52270e9i) q^{20} +2.82614e8 q^{21} +(1.61130e10 - 1.61130e10i) q^{22} +(-1.56435e10 - 1.56435e10i) q^{23} +(-2.53368e9 - 2.53368e9i) q^{24} -2.98272e9i q^{25} -1.17441e11i q^{26} +(2.51136e10 + 2.51136e10i) q^{27} +(-6.47382e9 - 6.47382e9i) q^{28} +(2.87513e10 - 2.87513e10i) q^{29} +6.62192e10 q^{30} +(-9.32340e10 + 9.32340e10i) q^{31} -2.67976e11i q^{32} -1.09282e11 q^{33} +(-4.44315e11 + 1.36106e11i) q^{34} +3.92698e10 q^{35} -5.38256e11i q^{36} +(2.66071e11 - 2.66071e11i) q^{37} -1.33843e12 q^{38} +(-3.98258e11 + 3.98258e11i) q^{39} +(-3.52060e11 - 3.52060e11i) q^{40} +(-9.16792e11 - 9.16792e11i) q^{41} +7.76236e10i q^{42} +1.52280e12i q^{43} +(2.50333e12 + 2.50333e12i) q^{44} +(1.63251e12 + 1.63251e12i) q^{45} +(4.29669e12 - 4.29669e12i) q^{46} -2.80714e12 q^{47} +(-6.06468e11 + 6.06468e11i) q^{48} -4.70153e12i q^{49} +8.19244e11 q^{50} +(1.96828e12 + 1.04518e12i) q^{51} +1.82458e13 q^{52} +5.81362e12i q^{53} +(-6.89777e12 + 6.89777e12i) q^{54} -1.51850e13 q^{55} +(4.12692e11 - 4.12692e11i) q^{56} +(4.53877e12 + 4.53877e12i) q^{57} +(7.89692e12 + 7.89692e12i) q^{58} +1.31219e13i q^{59} +1.02879e13i q^{60} +(1.54604e13 + 1.54604e13i) q^{61} +(-2.56080e13 - 2.56080e13i) q^{62} +(-1.91366e12 + 1.91366e12i) q^{63} +5.22673e13 q^{64} +(-5.53387e13 + 5.53387e13i) q^{65} -3.00158e13i q^{66} -7.02378e13 q^{67} +(-2.11456e13 - 6.90292e13i) q^{68} -2.91412e13 q^{69} +1.07860e13i q^{70} +(6.24763e13 - 6.24763e13i) q^{71} +3.43126e13 q^{72} +(5.34901e13 - 5.34901e13i) q^{73} +(7.30800e13 + 7.30800e13i) q^{74} +(-2.77816e12 - 2.77816e12i) q^{75} -2.07939e14i q^{76} -1.78002e13i q^{77} +(-1.09387e14 - 1.09387e14i) q^{78} +(6.74661e12 + 6.74661e12i) q^{79} +(-8.42699e13 + 8.42699e13i) q^{80} -1.34212e14 q^{81} +(2.51809e14 - 2.51809e14i) q^{82} +9.52151e13i q^{83} -1.20597e13 q^{84} +(2.73497e14 + 1.45229e14i) q^{85} -4.18258e14 q^{86} -5.35589e13i q^{87} +(-1.59582e14 + 1.59582e14i) q^{88} -5.02587e14 q^{89} +(-4.48391e14 + 4.48391e14i) q^{90} +(-6.48692e13 - 6.48692e13i) q^{91} +(6.67537e14 + 6.67537e14i) q^{92} +1.73680e14i q^{93} -7.71017e14i q^{94} +(6.30672e14 + 6.30672e14i) q^{95} +(-2.49598e14 - 2.49598e14i) q^{96} +(-8.48793e14 + 8.48793e14i) q^{97} +1.29134e15 q^{98} +(7.39984e14 - 7.39984e14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7}+O(q^{10}) $ 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7} + 8409498 q^{10} - 9729300 q^{11} - 82056486 q^{12} + 146863304 q^{13} - 1773752796 q^{14} + 16082152452 q^{16} + 1961077578 q^{17} - 7034899972 q^{18} + 21230427174 q^{20} - 47057263940 q^{21} - 3442343910 q^{22} - 15842736534 q^{23} + 94553484290 q^{24} - 294640558020 q^{27} - 17774164556 q^{28} + 102726169530 q^{29} - 643189839240 q^{30} - 385043642942 q^{31} + 2378676720192 q^{33} + 158249007174 q^{34} + 408521183892 q^{35} + 1375134180422 q^{37} + 1543745804832 q^{38} + 603440813444 q^{39} - 8303553806742 q^{40} + 1443758220300 q^{41} - 4657636435362 q^{44} + 6106558559866 q^{45} + 9604057332832 q^{46} - 21302607302640 q^{47} + 25515630744334 q^{48} - 18255254395212 q^{50} + 19158460873088 q^{51} - 48159060495244 q^{52} - 78998282739512 q^{54} + 13393057779764 q^{55} + 137860752160332 q^{56} + 31257866131908 q^{57} - 69211880377042 q^{58} + 38643830633662 q^{61} + 238390785941076 q^{62} - 71567394446902 q^{63} - 498262566925124 q^{64} + 178535375770548 q^{65} + 57983772499388 q^{67} + 261849713539554 q^{68} - 115652283503244 q^{69} - 44377197355566 q^{71} + 93677094320796 q^{72} + 405163878377696 q^{73} - 405068893451898 q^{74} + 225803653508132 q^{75} - 802546741257484 q^{78} - 155549526248110 q^{79} - 124920621818622 q^{80} - 10\!\cdots\!28 q^{81}+ \cdots + 173739293641872 q^{99}+O(q^{100}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7 + 8409498 * q^10 - 9729300 * q^11 - 82056486 * q^12 + 146863304 * q^13 - 1773752796 * q^14 + 16082152452 * q^16 + 1961077578 * q^17 - 7034899972 * q^18 + 21230427174 * q^20 - 47057263940 * q^21 - 3442343910 * q^22 - 15842736534 * q^23 + 94553484290 * q^24 - 294640558020 * q^27 - 17774164556 * q^28 + 102726169530 * q^29 - 643189839240 * q^30 - 385043642942 * q^31 + 2378676720192 * q^33 + 158249007174 * q^34 + 408521183892 * q^35 + 1375134180422 * q^37 + 1543745804832 * q^38 + 603440813444 * q^39 - 8303553806742 * q^40 + 1443758220300 * q^41 - 4657636435362 * q^44 + 6106558559866 * q^45 + 9604057332832 * q^46 - 21302607302640 * q^47 + 25515630744334 * q^48 - 18255254395212 * q^50 + 19158460873088 * q^51 - 48159060495244 * q^52 - 78998282739512 * q^54 + 13393057779764 * q^55 + 137860752160332 * q^56 + 31257866131908 * q^57 - 69211880377042 * q^58 + 38643830633662 * q^61 + 238390785941076 * q^62 - 71567394446902 * q^63 - 498262566925124 * q^64 + 178535375770548 * q^65 + 57983772499388 * q^67 + 261849713539554 * q^68 - 115652283503244 * q^69 - 44377197355566 * q^71 + 93677094320796 * q^72 + 405163878377696 * q^73 - 405068893451898 * q^74 + 225803653508132 * q^75 - 802546741257484 * q^78 - 155549526248110 * q^79 - 124920621818622 * q^80 - 1098726050204828 * q^81 - 575036459162320 * q^82 + 1901862557545176 * q^84 - 939038947054838 * q^85 + 1783857741230148 * q^86 + 1466099551935802 * q^88 - 1809234886116972 * q^89 - 156603181182342 * q^90 + 2736989931074496 * q^91 + 4441473764128152 * q^92 + 2349942705291804 * q^95 - 7961673687938290 * q^96 - 2718145106426904 * q^97 - 2118270343699824 * q^98 + 173739293641872 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			274.663i			1.51731i	0.651490	+	0.758657i	$0.274144\pi$
$2$			274.663i			1.51731i	−0.651490	+	0.758657i	$0.725856\pi$
$3$	931.417	−	931.417i	0.245887	−	0.245887i	−0.573393	−	0.819280i	$-0.694373\pi$
$3$	931.417	−	931.417i	0.245887	−	0.245887i	0.819280	+	0.573393i	$0.194373\pi$
$4$	−42671.9			−1.30224
$5$	129422.	−	129422.i	0.740857	−	0.740857i	−0.231886	−	0.972743i	$-0.574490\pi$
$5$	129422.	−	129422.i	0.740857	−	0.740857i	0.972743	+	0.231886i	$0.0744897\pi$
$6$	255826.	+	255826.i	0.373087	+	0.373087i
$7$	151712.	+	151712.i	0.0696279	+	0.0696279i	0.741063	−	0.671435i	$-0.234322\pi$
$7$	151712.	+	151712.i	0.0696279	+	0.0696279i	−0.671435	+	0.741063i	$0.734322\pi$
$8$		−	2.72024e6i		−	0.458598i
$9$			1.26138e7i			0.879080i
$10$	3.55476e7	+	3.55476e7i	1.12411	+	1.12411i
$11$	−5.86645e7	−	5.86645e7i	−0.907675	−	0.907675i	0.0884092	−	0.996084i	$-0.471822\pi$
$11$	−5.86645e7	−	5.86645e7i	−0.907675	−	0.907675i	−0.996084	+	0.0884092i	$0.971822\pi$
$12$	−3.97454e7	+	3.97454e7i	−0.320204	+	0.320204i
$13$	−4.27582e8			−1.88993			−0.944963	−	0.327178i	$-0.893902\pi$
$13$	−4.27582e8			−1.88993			−0.944963	+	0.327178i	$0.893902\pi$
$14$	−4.16696e7	+	4.16696e7i	−0.105647	+	0.105647i
$15$		−	2.41092e8i		−	0.364334i
$16$	−6.51123e8			−0.606406
$17$	4.95538e8	+	1.61767e9i	0.292894	+	0.956145i
$17$	4.95538e8	+	1.61767e9i	0.292894	+	0.956145i
$18$	−3.46456e9			−1.33384
$19$			4.87297e9i			1.25067i	0.780357	+	0.625334i	$0.215037\pi$
$19$			4.87297e9i			1.25067i	−0.780357	+	0.625334i	$0.784963\pi$
$20$	−5.52270e9	+	5.52270e9i	−0.964776	+	0.964776i
$21$	2.82614e8			0.0342412
$22$	1.61130e10	−	1.61130e10i	1.37723	−	1.37723i
$23$	−1.56435e10	−	1.56435e10i	−0.958019	−	0.958019i	0.0411344	−	0.999154i	$-0.486903\pi$
$23$	−1.56435e10	−	1.56435e10i	−0.958019	−	0.958019i	−0.999154	+	0.0411344i	$0.986903\pi$
$24$	−2.53368e9	−	2.53368e9i	−0.112763	−	0.112763i
$25$		−	2.98272e9i		−	0.0977378i
$26$		−	1.17441e11i		−	2.86761i
$27$	2.51136e10	+	2.51136e10i	0.462041	+	0.462041i
$28$	−6.47382e9	−	6.47382e9i	−0.0906725	−	0.0906725i
$29$	2.87513e10	−	2.87513e10i	0.309508	−	0.309508i	−0.535211	−	0.844719i	$-0.679768\pi$
$29$	2.87513e10	−	2.87513e10i	0.309508	−	0.309508i	0.844719	+	0.535211i	$0.179768\pi$
$30$	6.62192e10			0.552809
$31$	−9.32340e10	+	9.32340e10i	−0.608642	+	0.608642i	−0.942591	−	0.333949i	$-0.891619\pi$
$31$	−9.32340e10	+	9.32340e10i	−0.608642	+	0.608642i	0.333949	+	0.942591i	$0.391619\pi$
$32$		−	2.67976e11i		−	1.37871i
$33$	−1.09282e11			−0.446370
$34$	−4.44315e11	+	1.36106e11i	−1.45077	+	0.444412i
$35$	3.92698e10			0.103169
$36$		−	5.38256e11i		−	1.14478i
$37$	2.66071e11	−	2.66071e11i	0.460771	−	0.460771i	−0.438137	−	0.898908i	$-0.644362\pi$
$37$	2.66071e11	−	2.66071e11i	0.460771	−	0.460771i	0.898908	+	0.438137i	$0.144362\pi$
$38$	−1.33843e12			−1.89766
$39$	−3.98258e11	+	3.98258e11i	−0.464707	+	0.464707i
$40$	−3.52060e11	−	3.52060e11i	−0.339755	−	0.339755i
$41$	−9.16792e11	−	9.16792e11i	−0.735177	−	0.735177i	0.236463	−	0.971640i	$-0.424012\pi$
$41$	−9.16792e11	−	9.16792e11i	−0.735177	−	0.735177i	−0.971640	+	0.236463i	$0.924012\pi$
$42$			7.76236e10i			0.0519546i
$43$			1.52280e12i			0.854338i	0.904172	+	0.427169i	$0.140489\pi$
$43$			1.52280e12i			0.854338i	−0.904172	+	0.427169i	$0.859511\pi$
$44$	2.50333e12	+	2.50333e12i	1.18201	+	1.18201i
$45$	1.63251e12	+	1.63251e12i	0.651272	+	0.651272i
$46$	4.29669e12	−	4.29669e12i	1.45362	−	1.45362i
$47$	−2.80714e12			−0.808220			−0.404110	−	0.914710i	$-0.632419\pi$
$47$	−2.80714e12			−0.808220			−0.404110	+	0.914710i	$0.632419\pi$
$48$	−6.06468e11	+	6.06468e11i	−0.149107	+	0.149107i
$49$		−	4.70153e12i		−	0.990304i
$50$	8.19244e11			0.148299
$51$	1.96828e12	+	1.04518e12i	0.307122	+	0.163085i
$52$	1.82458e13			2.46114
$53$			5.81362e12i			0.679794i	0.940463	+	0.339897i	$0.110392\pi$
$53$			5.81362e12i			0.679794i	−0.940463	+	0.339897i	$0.889608\pi$
$54$	−6.89777e12	+	6.89777e12i	−0.701061	+	0.701061i
$55$	−1.51850e13			−1.34491
$56$	4.12692e11	−	4.12692e11i	0.0319312	−	0.0319312i
$57$	4.53877e12	+	4.53877e12i	0.307522	+	0.307522i
$58$	7.89692e12	+	7.89692e12i	0.469621	+	0.469621i
$59$			1.31219e13i			0.686444i	0.939254	+	0.343222i	$0.111518\pi$
$59$			1.31219e13i			0.686444i	−0.939254	+	0.343222i	$0.888482\pi$
$60$			1.02879e13i			0.474451i
$61$	1.54604e13	+	1.54604e13i	0.629865	+	0.629865i	0.948034	−	0.318169i	$-0.103068\pi$
$61$	1.54604e13	+	1.54604e13i	0.629865	+	0.629865i	−0.318169	+	0.948034i	$0.603068\pi$
$62$	−2.56080e13	−	2.56080e13i	−0.923501	−	0.923501i
$63$	−1.91366e12	+	1.91366e12i	−0.0612085	+	0.0612085i
$64$	5.22673e13			1.48553
$65$	−5.53387e13	+	5.53387e13i	−1.40016	+	1.40016i
$66$		−	3.00158e13i		−	0.677284i
$67$	−7.02378e13			−1.41583			−0.707913	−	0.706299i	$-0.750363\pi$
$67$	−7.02378e13			−1.41583			−0.707913	+	0.706299i	$0.750363\pi$
$68$	−2.11456e13	−	6.90292e13i	−0.381419	−	1.24513i
$69$	−2.91412e13			−0.471128
$70$			1.07860e13i			0.156539i
$71$	6.24763e13	−	6.24763e13i	0.815225	−	0.815225i	−0.170187	−	0.985412i	$-0.554437\pi$
$71$	6.24763e13	−	6.24763e13i	0.815225	−	0.815225i	0.985412	+	0.170187i	$0.0544370\pi$
$72$	3.43126e13			0.403144
$73$	5.34901e13	−	5.34901e13i	0.566698	−	0.566698i	−0.364504	−	0.931202i	$-0.618761\pi$
$73$	5.34901e13	−	5.34901e13i	0.566698	−	0.566698i	0.931202	+	0.364504i	$0.118761\pi$
$74$	7.30800e13	+	7.30800e13i	0.699134	+	0.699134i
$75$	−2.77816e12	−	2.77816e12i	−0.0240324	−	0.0240324i
$76$		−	2.07939e14i		−	1.62867i
$77$		−	1.78002e13i		−	0.126399i
$78$	−1.09387e14	−	1.09387e14i	−0.705107	−	0.705107i
$79$	6.74661e12	+	6.74661e12i	0.0395260	+	0.0395260i	0.726594	−	0.687068i	$-0.241102\pi$
$79$	6.74661e12	+	6.74661e12i	0.0395260	+	0.0395260i	−0.687068	+	0.726594i	$0.741102\pi$
$80$	−8.42699e13	+	8.42699e13i	−0.449260	+	0.449260i
$81$	−1.34212e14			−0.651860
$82$	2.51809e14	−	2.51809e14i	1.11549	−	1.11549i
$83$			9.52151e13i			0.385141i	0.981283	+	0.192571i	$0.0616825\pi$
$83$			9.52151e13i			0.385141i	−0.981283	+	0.192571i	$0.938318\pi$
$84$	−1.20597e13			−0.0445903
$85$	2.73497e14	+	1.45229e14i	0.925359	+	0.491374i
$86$	−4.18258e14			−1.29630
$87$		−	5.35589e13i		−	0.152208i
$88$	−1.59582e14	+	1.59582e14i	−0.416258	+	0.416258i
$89$	−5.02587e14			−1.20444			−0.602221	−	0.798330i	$-0.705717\pi$
$89$	−5.02587e14			−1.20444			−0.602221	+	0.798330i	$0.705717\pi$
$90$	−4.48391e14	+	4.48391e14i	−0.988185	+	0.988185i
$91$	−6.48692e13	−	6.48692e13i	−0.131592	−	0.131592i
$92$	6.67537e14	+	6.67537e14i	1.24757	+	1.24757i
$93$			1.73680e14i			0.299314i
$94$		−	7.71017e14i		−	1.22632i
$95$	6.30672e14	+	6.30672e14i	0.926566	+	0.926566i
$96$	−2.49598e14	−	2.49598e14i	−0.339005	−	0.339005i
$97$	−8.48793e14	+	8.48793e14i	−1.06663	+	1.06663i	−0.0690141	+	0.997616i	$0.521985\pi$
$97$	−8.48793e14	+	8.48793e14i	−1.06663	+	1.06663i	−0.997616	+	0.0690141i	$0.978015\pi$
$98$	1.29134e15			1.50260
$99$	7.39984e14	−	7.39984e14i	0.797919	−	0.797919i
$100$			1.27278e14i			0.127278i
$101$	1.12095e15			1.04034			0.520168	−	0.854064i	$-0.325869\pi$
$101$	1.12095e15			1.04034			0.520168	+	0.854064i	$0.325869\pi$
$102$	−2.87071e14	+	5.40615e14i	−0.247451	+	0.466001i
$103$	1.34332e15			1.07622			0.538108	−	0.842876i	$-0.319139\pi$
$103$	1.34332e15			1.07622			0.538108	+	0.842876i	$0.319139\pi$
$104$			1.16313e15i			0.866716i
$105$	3.65765e13	−	3.65765e13i	0.0253678	−	0.0253678i
$106$	−1.59679e15			−1.03146
$107$	1.27478e15	−	1.27478e15i	0.767460	−	0.767460i	−0.210199	−	0.977659i	$-0.567411\pi$
$107$	1.27478e15	−	1.27478e15i	0.767460	−	0.767460i	0.977659	+	0.210199i	$0.0674111\pi$
$108$	−1.07164e15	−	1.07164e15i	−0.601689	−	0.601689i
$109$	1.26804e15	+	1.26804e15i	0.664409	+	0.664409i	0.956416	−	0.292007i	$-0.0943231\pi$
$109$	1.26804e15	+	1.26804e15i	0.664409	+	0.664409i	−0.292007	+	0.956416i	$0.594323\pi$
$110$		−	4.17076e15i		−	2.04066i
$111$		−	4.95647e14i		−	0.226595i
$112$	−9.87830e13	−	9.87830e13i	−0.0422228	−	0.0422228i
$113$	2.84842e15	+	2.84842e15i	1.13898	+	1.13898i	0.988634	+	0.150343i	$0.0480379\pi$
$113$	2.84842e15	+	2.84842e15i	1.13898	+	1.13898i	0.150343	+	0.988634i	$0.451962\pi$
$114$	−1.24663e15	+	1.24663e15i	−0.466608	+	0.466608i
$115$	−4.04923e15			−1.41951
$116$	−1.22687e15	+	1.22687e15i	−0.403055	+	0.403055i
$117$		−	5.39345e15i		−	1.66139i
$118$	−3.60409e15			−1.04155
$119$	−1.70241e14	+	3.20599e14i	−0.0461808	+	0.0869680i
$120$	−6.55829e14			−0.167083
$121$			2.70580e15i			0.647748i
$122$	−4.24641e15	+	4.24641e15i	−0.955703	+	0.955703i
$123$	−1.70783e15			−0.361540
$124$	3.97847e15	−	3.97847e15i	0.792600	−	0.792600i
$125$	3.56363e15	+	3.56363e15i	0.668447	+	0.668447i
$126$	−5.25613e14	−	5.25613e14i	−0.0928725	−	0.0928725i
$127$		−	4.11947e15i		−	0.685983i	−0.939339	−	0.342991i	$-0.888560\pi$
$127$		−	4.11947e15i		−	0.685983i	0.939339	−	0.342991i	$-0.111440\pi$
$128$			5.57485e15i			0.875303i
$129$	1.41836e15	+	1.41836e15i	0.210070	+	0.210070i
$130$	−1.51995e16	−	1.51995e16i	−2.12449	−	2.12449i
$131$	−4.43086e15	+	4.43086e15i	−0.584727	+	0.584727i	−0.936199	−	0.351471i	$-0.885681\pi$
$131$	−4.43086e15	+	4.43086e15i	−0.584727	+	0.584727i	0.351471	+	0.936199i	$0.385681\pi$
$132$	4.66328e15			0.581283
$133$	−7.39286e14	+	7.39286e14i	−0.0870814	+	0.0870814i
$134$		−	1.92918e16i		−	2.14825i
$135$	6.50051e15			0.684612
$136$	4.40046e15	−	1.34798e15i	0.438486	−	0.134321i
$137$	8.09081e15			0.763111			0.381555	−	0.924346i	$-0.375389\pi$
$137$	8.09081e15			0.763111			0.381555	+	0.924346i	$0.375389\pi$
$138$		−	8.00401e15i		−	0.714850i
$139$	9.49499e13	−	9.49499e13i	0.00803310	−	0.00803310i	−0.703079	−	0.711112i	$-0.748192\pi$
$139$	9.49499e13	−	9.49499e13i	0.00803310	−	0.00803310i	0.711112	+	0.703079i	$0.248192\pi$
$140$	−1.67572e15			−0.134351
$141$	−2.61462e15	+	2.61462e15i	−0.198730	+	0.198730i
$142$	1.71599e16	+	1.71599e16i	1.23695	+	1.23695i
$143$	2.50839e16	+	2.50839e16i	1.71544	+	1.71544i
$144$		−	8.21316e15i		−	0.533079i
$145$		−	7.44212e15i		−	0.458602i
$146$	1.46918e16	+	1.46918e16i	0.859859	+	0.859859i
$147$	−4.37909e15	−	4.37909e15i	−0.243502	−	0.243502i
$148$	−1.13538e16	+	1.13538e16i	−0.600036	+	0.600036i
$149$	−2.71816e16			−1.36577			−0.682885	−	0.730526i	$-0.739275\pi$
$149$	−2.71816e16			−1.36577			−0.682885	+	0.730526i	$0.739275\pi$
$150$	7.63058e14	−	7.63058e14i	0.0364647	−	0.0364647i
$151$			3.34694e16i			1.52167i	0.648945	+	0.760835i	$0.275211\pi$
$151$			3.34694e16i			1.52167i	−0.648945	+	0.760835i	$0.724789\pi$
$152$	1.32556e16			0.573554
$153$	−2.04050e16	+	6.25063e15i	−0.840527	+	0.257477i
$154$	4.88905e15			0.191787
$155$			2.41331e16i			0.901833i
$156$	1.69944e16	−	1.69944e16i	0.605162	−	0.605162i
$157$	−2.01531e16			−0.684060			−0.342030	−	0.939689i	$-0.611114\pi$
$157$	−2.01531e16			−0.684060			−0.342030	+	0.939689i	$0.611114\pi$
$158$	−1.85305e15	+	1.85305e15i	−0.0599733	+	0.0599733i
$159$	5.41490e15	+	5.41490e15i	0.167152	+	0.167152i
$160$	−3.46821e16	−	3.46821e16i	−1.02142	−	1.02142i
$161$		−	4.74659e15i		−	0.133410i
$162$		−	3.68632e16i		−	0.989077i
$163$	−2.51864e16	−	2.51864e16i	−0.645296	−	0.645296i	0.306556	−	0.951853i	$-0.400823\pi$
$163$	−2.51864e16	−	2.51864e16i	−0.645296	−	0.645296i	−0.951853	+	0.306556i	$0.900823\pi$
$164$	3.91213e16	+	3.91213e16i	0.957379	+	0.957379i
$165$	−1.41436e16	+	1.41436e16i	−0.330696	+	0.330696i
$166$	−2.61521e16			−0.584380
$167$	−5.66044e15	+	5.66044e15i	−0.120914	+	0.120914i	−0.764975	−	0.644060i	$-0.777248\pi$
$167$	−5.66044e15	+	5.66044e15i	−0.120914	+	0.120914i	0.644060	+	0.764975i	$0.277248\pi$
$168$		−	7.68777e14i		−	0.0157029i
$169$	1.31641e17			2.57182
$170$	−3.98892e16	+	7.51195e16i	−0.745569	+	1.40406i
$171$	−6.14668e16			−1.09944
$172$		−	6.49808e16i		−	1.11256i
$173$	4.57552e16	−	4.57552e16i	0.750058	−	0.750058i	−0.224431	−	0.974490i	$-0.572052\pi$
$173$	4.57552e16	−	4.57552e16i	0.750058	−	0.750058i	0.974490	+	0.224431i	$0.0720525\pi$
$174$	1.47107e16			0.230947
$175$	4.52513e14	−	4.52513e14i	0.00680528	−	0.00680528i
$176$	3.81978e16	+	3.81978e16i	0.550419	+	0.550419i
$177$	1.22219e16	+	1.22219e16i	0.168787	+	0.168787i
$178$		−	1.38042e17i		−	1.82752i
$179$			3.31655e16i			0.421006i	0.977593	+	0.210503i	$0.0675102\pi$
$179$			3.31655e16i			0.421006i	−0.977593	+	0.210503i	$0.932490\pi$
$180$	−6.96624e16	−	6.96624e16i	−0.848115	−	0.848115i
$181$	−6.58404e16	−	6.58404e16i	−0.768958	−	0.768958i	0.208965	−	0.977923i	$-0.432991\pi$
$181$	−6.58404e16	−	6.58404e16i	−0.768958	−	0.768958i	−0.977923	+	0.208965i	$0.932991\pi$
$182$	1.78172e16	−	1.78172e16i	0.199666	−	0.199666i
$183$	2.88002e16			0.309751
$184$	−4.25540e16	+	4.25540e16i	−0.439346	+	0.439346i
$185$		−	6.88711e16i		−	0.682731i
$186$	−4.77034e16			−0.454153
$187$	6.58295e16	−	1.23970e17i	0.602017	−	1.13372i
$188$	1.19786e17			1.05250
$189$			7.62004e15i			0.0643419i
$190$	−1.73222e17	+	1.73222e17i	−1.40589	+	1.40589i
$191$	−2.30753e16			−0.180052			−0.0900258	−	0.995939i	$-0.528695\pi$
$191$	−2.30753e16			−0.180052			−0.0900258	+	0.995939i	$0.528695\pi$
$192$	4.86826e16	−	4.86826e16i	0.365271	−	0.365271i
$193$	−3.53924e16	−	3.53924e16i	−0.255405	−	0.255405i	0.567777	−	0.823182i	$-0.307804\pi$
$193$	−3.53924e16	−	3.53924e16i	−0.255405	−	0.255405i	−0.823182	+	0.567777i	$0.807804\pi$
$194$	−2.33132e17	−	2.33132e17i	−1.61841	−	1.61841i
$195$			1.03087e17i			0.688563i
$196$			2.00623e17i			1.28962i
$197$	1.00560e17	+	1.00560e17i	0.622199	+	0.622199i	0.946093	−	0.323895i	$-0.104992\pi$
$197$	1.00560e17	+	1.00560e17i	0.622199	+	0.622199i	−0.323895	+	0.946093i	$0.604992\pi$
$198$	2.03246e17	+	2.03246e17i	1.21069	+	1.21069i
$199$	−6.56932e16	+	6.56932e16i	−0.376810	+	0.376810i	−0.869950	−	0.493140i	$-0.835849\pi$
$199$	−6.56932e16	+	6.56932e16i	−0.376810	+	0.376810i	0.493140	+	0.869950i	$0.335849\pi$
$200$	−8.11371e15			−0.0448223
$201$	−6.54207e16	+	6.54207e16i	−0.348133	+	0.348133i
$202$			3.07882e17i			1.57852i
$203$	8.72380e15			0.0431008
$204$	−8.39903e16	−	4.45996e16i	−0.399947	−	0.212376i
$205$	−2.37307e17			−1.08932
$206$			3.68960e17i			1.63296i
$207$	1.97324e17	−	1.97324e17i	0.842175	−	0.842175i
$208$	2.78409e17			1.14606
$209$	2.85871e17	−	2.85871e17i	1.13520	−	1.13520i
$210$	1.00462e16	+	1.00462e16i	0.0384909	+	0.0384909i
$211$	−2.38588e17	−	2.38588e17i	−0.882124	−	0.882124i	0.111627	−	0.993750i	$-0.464394\pi$
$211$	−2.38588e17	−	2.38588e17i	−0.882124	−	0.882124i	−0.993750	+	0.111627i	$0.964394\pi$
$212$		−	2.48078e17i		−	0.885257i
$213$		−	1.16383e17i		−	0.400906i
$214$	3.50134e17	+	3.50134e17i	1.16448	+	1.16448i
$215$	1.97085e17	+	1.97085e17i	0.632942	+	0.632942i
$216$	6.83149e16	−	6.83149e16i	0.211891	−	0.211891i
$217$	−2.82894e16			−0.0847569
$218$	−3.48285e17	+	3.48285e17i	−1.00812	+	1.00812i
$219$		−	9.96431e16i		−	0.278687i
$220$	6.47973e17			1.75141
$221$	−2.11883e17	−	6.91688e17i	−0.553547	−	1.80704i
$222$	1.36136e17			0.343816
$223$		−	1.79403e17i		−	0.438069i	−0.975717	−	0.219034i	$-0.929709\pi$
$223$		−	1.79403e17i		−	0.438069i	0.975717	−	0.219034i	$-0.0702907\pi$
$224$	4.06551e16	−	4.06551e16i	0.0959965	−	0.0959965i
$225$	3.76235e16			0.0859193
$226$	−7.82355e17	+	7.82355e17i	−1.72819	+	1.72819i
$227$	2.82304e17	+	2.82304e17i	0.603286	+	0.603286i	0.941183	−	0.337897i	$-0.109716\pi$
$227$	2.82304e17	+	2.82304e17i	0.603286	+	0.603286i	−0.337897	+	0.941183i	$0.609716\pi$
$228$	−1.93678e17	−	1.93678e17i	−0.400469	−	0.400469i
$229$			6.66106e17i			1.33284i	0.745578	+	0.666419i	$0.232174\pi$
$229$			6.66106e17i			1.33284i	−0.745578	+	0.666419i	$0.767826\pi$
$230$		−	1.11217e18i		−	2.15384i
$231$	−1.65794e16	−	1.65794e16i	−0.0310798	−	0.0310798i
$232$	−7.82103e16	−	7.82103e16i	−0.141940	−	0.141940i
$233$	8.97112e16	−	8.97112e16i	0.157644	−	0.157644i	−0.623878	−	0.781522i	$-0.714444\pi$
$233$	8.97112e16	−	8.97112e16i	0.157644	−	0.157644i	0.781522	+	0.623878i	$0.214444\pi$
$234$	1.48138e18			2.52086
$235$	−3.63306e17	+	3.63306e17i	−0.598775	+	0.598775i
$236$		−	5.59934e17i		−	0.893917i
$237$	1.25678e16			0.0194378
$238$	−8.80567e16	−	4.67589e16i	−0.131958	−	0.0700708i
$239$	−1.20595e18			−1.75123			−0.875616	−	0.483008i	$-0.839544\pi$
$239$	−1.20595e18			−1.75123			−0.875616	+	0.483008i	$0.839544\pi$
$240$			1.56981e17i			0.220934i
$241$	−6.14877e17	+	6.14877e17i	−0.838804	+	0.838804i	−0.988702	−	0.149897i	$-0.952106\pi$
$241$	−6.14877e17	+	6.14877e17i	−0.838804	+	0.838804i	0.149897	+	0.988702i	$0.452106\pi$
$242$	−7.43185e17			−0.982837
$243$	−4.85360e17	+	4.85360e17i	−0.622324	+	0.622324i
$244$	−6.59725e17	−	6.59725e17i	−0.820237	−	0.820237i
$245$	−6.08483e17	−	6.08483e17i	−0.733673	−	0.733673i
$246$		−	4.69079e17i		−	0.548571i
$247$		−	2.08360e18i		−	2.36367i
$248$	2.53619e17	+	2.53619e17i	0.279122	+	0.279122i
$249$	8.86850e16	+	8.86850e16i	0.0947011	+	0.0947011i
$250$	−9.78797e17	+	9.78797e17i	−1.01424	+	1.01424i
$251$	3.39582e17			0.341501			0.170750	−	0.985314i	$-0.445381\pi$
$251$	3.39582e17			0.341501			0.170750	+	0.985314i	$0.445381\pi$
$252$	8.16597e16	−	8.16597e16i	0.0797083	−	0.0797083i
$253$			1.83543e18i			1.73914i
$254$	1.13147e18			1.04085
$255$	3.90009e17	−	1.19471e17i	0.348356	−	0.106711i
$256$	1.81488e17			0.157416
$257$			8.40430e17i			0.707951i	0.935255	+	0.353975i	$0.115170\pi$
$257$			8.40430e17i			0.707951i	−0.935255	+	0.353975i	$0.884830\pi$
$258$	−3.89572e17	+	3.89572e17i	−0.318743	+	0.318743i
$259$	8.07322e16			0.0641650
$260$	2.36141e18	−	2.36141e18i	1.82335	−	1.82335i
$261$	3.62664e17	+	3.62664e17i	0.272082	+	0.272082i
$262$	−1.21699e18	−	1.21699e18i	−0.887215	−	0.887215i
$263$		−	1.15668e18i		−	0.819489i	−0.912200	−	0.409745i	$-0.865618\pi$
$263$		−	1.15668e18i		−	0.819489i	0.912200	−	0.409745i	$-0.134382\pi$
$264$			2.97274e17i			0.204705i
$265$	7.52412e17	+	7.52412e17i	0.503630	+	0.503630i
$266$	−2.03055e17	−	2.03055e17i	−0.132130	−	0.132130i
$267$	−4.68118e17	+	4.68118e17i	−0.296156	+	0.296156i
$268$	2.99718e18			1.84375
$269$	−2.43591e17	+	2.43591e17i	−0.145720	+	0.145720i	−0.776203	−	0.630483i	$-0.782857\pi$
$269$	−2.43591e17	+	2.43591e17i	−0.145720	+	0.145720i	0.630483	+	0.776203i	$0.282857\pi$
$270$			1.78545e18i			1.03877i
$271$	1.94034e18			1.09801			0.549007	−	0.835818i	$-0.315006\pi$
$271$	1.94034e18			1.09801			0.549007	+	0.835818i	$0.315006\pi$
$272$	−3.22656e17	−	1.05330e18i	−0.177612	−	0.579812i
$273$	−1.20841e17			−0.0647132
$274$			2.22225e18i			1.15788i
$275$	−1.74980e17	+	1.74980e17i	−0.0887141	+	0.0887141i
$276$	1.24351e18			0.613524
$277$	1.33455e18	−	1.33455e18i	0.640821	−	0.640821i	−0.309936	−	0.950757i	$-0.600308\pi$
$277$	1.33455e18	−	1.33455e18i	0.640821	−	0.640821i	0.950757	+	0.309936i	$0.100308\pi$
$278$	2.60792e16	+	2.60792e16i	0.0121887	+	0.0121887i
$279$	−1.17604e18	−	1.17604e18i	−0.535044	−	0.535044i
$280$		−	1.06823e17i		−	0.0473129i
$281$		−	5.85437e17i		−	0.252454i	−0.992001	−	0.126227i	$-0.959713\pi$
$281$		−	5.85437e17i		−	0.252454i	0.992001	−	0.126227i	$-0.0402868\pi$
$282$	−7.18139e17	−	7.18139e17i	−0.301537	−	0.301537i
$283$	−7.41082e17	−	7.41082e17i	−0.303018	−	0.303018i	0.539176	−	0.842193i	$-0.318736\pi$
$283$	−7.41082e17	−	7.41082e17i	−0.303018	−	0.303018i	−0.842193	+	0.539176i	$0.818736\pi$
$284$	−2.66598e18	+	2.66598e18i	−1.06162	+	1.06162i
$285$	1.17484e18			0.455660
$286$	−6.88963e18	+	6.88963e18i	−2.60286	+	2.60286i
$287$		−	2.78176e17i		−	0.102378i
$288$	3.38021e18			1.21199
$289$	−2.37131e18	+	1.60324e18i	−0.828426	+	0.560098i
$290$	2.04408e18			0.695844
$291$			1.58116e18i			0.524540i
$292$	−2.28252e18	+	2.28252e18i	−0.737978	+	0.737978i
$293$	6.31180e17			0.198905			0.0994526	−	0.995042i	$-0.468291\pi$
$293$	6.31180e17			0.198905			0.0994526	+	0.995042i	$0.468291\pi$
$294$	1.20277e18	−	1.20277e18i	0.369470	−	0.369470i
$295$	1.69826e18	+	1.69826e18i	0.508557	+	0.508557i
$296$	−7.23777e17	−	7.23777e17i	−0.211309	−	0.211309i
$297$		−	2.94655e18i		−	0.838765i
$298$		−	7.46578e18i		−	2.07230i
$299$	6.68887e18	+	6.68887e18i	1.81058	+	1.81058i
$300$	1.18549e17	+	1.18549e17i	0.0312960	+	0.0312960i
$301$	−2.31027e17	+	2.31027e17i	−0.0594858	+	0.0594858i
$302$	−9.19281e18			−2.30885
$303$	1.04407e18	−	1.04407e18i	0.255805	−	0.255805i
$304$		−	3.17291e18i		−	0.758412i
$305$	4.00185e18			0.933279
$306$	−1.71682e18	−	5.60452e18i	−0.390673	−	1.27534i
$307$	−2.64025e18			−0.586282			−0.293141	−	0.956069i	$-0.594701\pi$
$307$	−2.64025e18			−0.586282			−0.293141	+	0.956069i	$0.594701\pi$
$308$			7.59567e17i			0.164602i
$309$	1.25119e18	−	1.25119e18i	0.264627	−	0.264627i
$310$	−6.62849e18			−1.36836
$311$	4.79266e18	−	4.79266e18i	0.965769	−	0.965769i	−0.0336641	−	0.999433i	$-0.510718\pi$
$311$	4.79266e18	−	4.79266e18i	0.965769	−	0.965769i	0.999433	+	0.0336641i	$0.0107176\pi$
$312$	1.08336e18	+	1.08336e18i	0.213114	+	0.213114i
$313$	−1.09085e17	−	1.09085e17i	−0.0209499	−	0.0209499i	0.696554	−	0.717504i	$-0.254716\pi$
$313$	−1.09085e17	−	1.09085e17i	−0.0209499	−	0.0209499i	−0.717504	+	0.696554i	$0.754716\pi$
$314$		−	5.53531e18i		−	1.03793i
$315$			4.95342e17i			0.0906935i
$316$	−2.87891e17	−	2.87891e17i	−0.0514724	−	0.0514724i
$317$	8.79993e17	+	8.79993e17i	0.153651	+	0.153651i	0.779746	−	0.626096i	$-0.215348\pi$
$317$	8.79993e17	+	8.79993e17i	0.153651	+	0.153651i	−0.626096	+	0.779746i	$0.715348\pi$
$318$	−1.48727e18	+	1.48727e18i	−0.253623	+	0.253623i
$319$	−3.37336e18			−0.561866
$320$	6.76455e18	−	6.76455e18i	1.10056	−	1.10056i
$321$		−	2.37470e18i		−	0.377416i
$322$	1.30371e18			0.202425
$323$	−7.88287e18	+	2.41474e18i	−1.19582	+	0.366313i
$324$	5.72709e18			0.848881
$325$			1.27536e18i			0.184717i
$326$	6.91778e18	−	6.91778e18i	0.979117	−	0.979117i
$327$	2.36216e18			0.326739
$328$	−2.49389e18	+	2.49389e18i	−0.337151	+	0.337151i
$329$	−4.25875e17	−	4.25875e17i	−0.0562747	−	0.0562747i
$330$	−3.88472e18	−	3.88472e18i	−0.501771	−	0.501771i
$331$		−	1.62647e18i		−	0.205370i	−0.994714	−	0.102685i	$-0.967257\pi$
$331$		−	1.62647e18i		−	0.205370i	0.994714	−	0.102685i	$-0.0327433\pi$
$332$		−	4.06301e18i		−	0.501548i
$333$	3.35618e18	+	3.35618e18i	0.405054	+	0.405054i
$334$	−1.55472e18	−	1.55472e18i	−0.183465	−	0.183465i
$335$	−9.09035e18	+	9.09035e18i	−1.04892	+	1.04892i
$336$	−1.84016e17			−0.0207640
$337$	−7.00791e18	+	7.00791e18i	−0.773329	+	0.773329i	−0.978687	−	0.205358i	$-0.934164\pi$
$337$	−7.00791e18	+	7.00791e18i	−0.773329	+	0.773329i	0.205358	+	0.978687i	$0.434164\pi$
$338$			3.61569e19i			3.90226i
$339$	5.30613e18			0.560118
$340$	−1.16706e19	−	6.19721e18i	−1.20504	−	0.639889i
$341$	1.09391e19			1.10490
$342$		−	1.68827e19i		−	1.66819i
$343$	1.43354e18	−	1.43354e18i	0.138581	−	0.138581i
$344$	4.14238e18			0.391798
$345$	−3.77152e18	+	3.77152e18i	−0.349039	+	0.349039i
$346$	1.25673e19	+	1.25673e19i	1.13807	+	1.13807i
$347$	−7.03755e18	−	7.03755e18i	−0.623664	−	0.623664i	0.322802	−	0.946466i	$-0.395375\pi$
$347$	−7.03755e18	−	7.03755e18i	−0.623664	−	0.623664i	−0.946466	+	0.322802i	$0.895375\pi$
$348$			2.28546e18i			0.198212i
$349$			1.60544e19i			1.36271i	0.731955	+	0.681353i	$0.238608\pi$
$349$			1.60544e19i			1.36271i	−0.731955	+	0.681353i	$0.761392\pi$
$350$	1.24289e17	+	1.24289e17i	0.0103257	+	0.0103257i
$351$	−1.07381e19	−	1.07381e19i	−0.873222	−	0.873222i
$352$	−1.57207e19	+	1.57207e19i	−1.25142	+	1.25142i
$353$	1.09393e19			0.852471			0.426236	−	0.904612i	$-0.359839\pi$
$353$	1.09393e19			0.852471			0.426236	+	0.904612i	$0.359839\pi$
$354$	−3.35691e18	+	3.35691e18i	−0.256104	+	0.256104i
$355$		−	1.61717e19i		−	1.20793i
$356$	2.14463e19			1.56848
$357$	1.40046e17	+	4.57176e17i	0.0100290	+	0.0327395i
$358$	−9.10934e18			−0.638799
$359$			1.59137e19i			1.09286i	0.837505	+	0.546429i	$0.184013\pi$
$359$			1.59137e19i			1.09286i	−0.837505	+	0.546429i	$0.815987\pi$
$360$	4.44082e18	−	4.44082e18i	0.298672	−	0.298672i
$361$	−8.56473e18			−0.564170
$362$	1.80839e19	−	1.80839e19i	1.16675	−	1.16675i
$363$	2.52023e18	+	2.52023e18i	0.159273	+	0.159273i
$364$	2.76809e18	+	2.76809e18i	0.171364	+	0.171364i
$365$		−	1.38456e19i		−	0.839684i
$366$			7.91036e18i			0.469989i
$367$	−1.06697e19	−	1.06697e19i	−0.621095	−	0.621095i	0.324716	−	0.945811i	$-0.394731\pi$
$367$	−1.06697e19	−	1.06697e19i	−0.621095	−	0.621095i	−0.945811	+	0.324716i	$0.894731\pi$
$368$	1.01858e19	+	1.01858e19i	0.580948	+	0.580948i
$369$	1.15643e19	−	1.15643e19i	0.646279	−	0.646279i
$370$	1.89164e19			1.03592
$371$	−8.81993e17	+	8.81993e17i	−0.0473326	+	0.0473326i
$372$		−	7.41124e18i		−	0.389779i
$373$	−7.42445e18			−0.382691			−0.191345	−	0.981523i	$-0.561285\pi$
$373$	−7.42445e18			−0.382691			−0.191345	+	0.981523i	$0.561285\pi$
$374$	3.40501e19	+	1.80809e19i	1.72021	+	0.913448i
$375$	6.63845e18			0.328724
$376$			7.63608e18i			0.370648i
$377$	−1.22935e19	+	1.22935e19i	−0.584947	+	0.584947i
$378$	−2.09294e18			−0.0976268
$379$	−7.82773e18	+	7.82773e18i	−0.357966	+	0.357966i	−0.863063	−	0.505097i	$-0.831457\pi$
$379$	−7.82773e18	+	7.82773e18i	−0.357966	+	0.357966i	0.505097	+	0.863063i	$0.331457\pi$
$380$	−2.69120e19	−	2.69120e19i	−1.20661	−	1.20661i
$381$	−3.83694e18	−	3.83694e18i	−0.168674	−	0.168674i
$382$		−	6.33793e18i		−	0.273195i
$383$		−	5.51527e18i		−	0.233118i	−0.993184	−	0.116559i	$-0.962814\pi$
$383$		−	5.51527e18i		−	0.233118i	0.993184	−	0.116559i	$-0.0371865\pi$
$384$	5.19251e18	+	5.19251e18i	0.215225	+	0.215225i
$385$	−2.30374e18	−	2.30374e18i	−0.0936436	−	0.0936436i
$386$	9.72098e18	−	9.72098e18i	0.387530	−	0.387530i
$387$	−1.92084e19			−0.751031
$388$	3.62196e19	−	3.62196e19i	1.38901	−	1.38901i
$389$			3.54519e19i			1.33357i	0.745248	+	0.666787i	$0.232331\pi$
$389$			3.54519e19i			1.33357i	−0.745248	+	0.666787i	$0.767669\pi$
$390$	−2.83142e19			−1.04477
$391$	1.75541e19	−	3.30579e19i	0.635407	−	1.19660i
$392$	−1.27893e19			−0.454151
$393$			8.25396e18i			0.287553i
$394$	−2.76202e19	+	2.76202e19i	−0.944071	+	0.944071i
$395$	1.74632e18			0.0585662
$396$	−3.15765e19	+	3.15765e19i	−1.03908	+	1.03908i
$397$	−3.19850e19	−	3.19850e19i	−1.03280	−	1.03280i	−0.999443	−	0.0333582i	$-0.989380\pi$
$397$	−3.19850e19	−	3.19850e19i	−1.03280	−	1.03280i	−0.0333582	−	0.999443i	$-0.510620\pi$
$398$	−1.80435e19	−	1.80435e19i	−0.571739	−	0.571739i
$399$			1.37717e18i			0.0428243i
$400$			1.94212e18i			0.0592688i
$401$	−1.16851e19	−	1.16851e19i	−0.349985	−	0.349985i	0.510119	−	0.860104i	$-0.329601\pi$
$401$	−1.16851e19	−	1.16851e19i	−0.349985	−	0.349985i	−0.860104	+	0.510119i	$0.829601\pi$
$402$	−1.79687e19	−	1.79687e19i	−0.528227	−	0.528227i
$403$	3.98652e19	−	3.98652e19i	1.15029	−	1.15029i
$404$	−4.78329e19			−1.35477
$405$	−1.73701e19	+	1.73701e19i	−0.482935	+	0.482935i
$406$			2.39611e18i			0.0653975i
$407$	−3.12179e19			−0.836460
$408$	2.84313e18	−	5.35420e18i	0.0747903	−	0.140846i
$409$	5.68775e19			1.46898			0.734489	−	0.678621i	$-0.237422\pi$
$409$	5.68775e19			1.46898			0.734489	+	0.678621i	$0.237422\pi$
$410$		−	6.51795e19i		−	1.65284i
$411$	7.53592e18	−	7.53592e18i	0.187639	−	0.187639i
$412$	−5.73219e19			−1.40149
$413$	−1.99074e18	+	1.99074e18i	−0.0477957	+	0.0477957i
$414$	5.41977e19	+	5.41977e19i	1.27784	+	1.27784i
$415$	1.23230e19	+	1.23230e19i	0.285335	+	0.285335i
$416$			1.14582e20i			2.60565i
$417$		−	1.76876e17i		−	0.00395047i
$418$	7.85181e19	+	7.85181e19i	1.72246	+	1.72246i
$419$	−9.85081e18	−	9.85081e18i	−0.212259	−	0.212259i	0.592967	−	0.805227i	$-0.297956\pi$
$419$	−9.85081e18	−	9.85081e18i	−0.212259	−	0.212259i	−0.805227	+	0.592967i	$0.797956\pi$
$420$	−1.56079e18	+	1.56079e18i	−0.0330350	+	0.0330350i
$421$	1.74513e19			0.362838			0.181419	−	0.983406i	$-0.441931\pi$
$421$	1.74513e19			0.362838			0.181419	+	0.983406i	$0.441931\pi$
$422$	6.55313e19	−	6.55313e19i	1.33846	−	1.33846i
$423$		−	3.54087e19i		−	0.710490i
$424$	1.58144e19			0.311752
$425$	4.82507e18	−	1.47805e18i	0.0934515	−	0.0286268i
$426$	3.19661e19			0.608300
$427$			4.69105e18i			0.0877124i
$428$	−5.43971e19	+	5.43971e19i	−0.999419	+	0.999419i
$429$	4.67272e19			0.843606
$430$	−5.41319e19	+	5.41319e19i	−0.960372	+	0.960372i
$431$	−5.31203e19	−	5.31203e19i	−0.926150	−	0.926150i	0.0713050	−	0.997455i	$-0.477284\pi$
$431$	−5.31203e19	−	5.31203e19i	−0.926150	−	0.926150i	−0.997455	+	0.0713050i	$0.977284\pi$
$432$	−1.63520e19	−	1.63520e19i	−0.280184	−	0.280184i
$433$			5.32361e19i			0.896494i	0.893910	+	0.448247i	$0.147951\pi$
$433$			5.32361e19i			0.896494i	−0.893910	+	0.448247i	$0.852049\pi$
$434$		−	7.77005e18i		−	0.128603i
$435$	−6.93172e18	−	6.93172e18i	−0.112764	−	0.112764i
$436$	−5.41098e19	−	5.41098e19i	−0.865222	−	0.865222i
$437$	7.62302e19	−	7.62302e19i	1.19816	−	1.19816i
$438$	2.73683e19			0.422856
$439$	8.16562e19	−	8.16562e19i	1.24024	−	1.24024i	0.280338	−	0.959901i	$-0.409554\pi$
$439$	8.16562e19	−	8.16562e19i	1.24024	−	1.24024i	0.959901	−	0.280338i	$-0.0904465\pi$
$440$			4.13068e19i			0.616775i
$441$	5.93043e19			0.870556
$442$	1.89981e20	−	5.81966e19i	2.74185	−	0.839905i
$443$	−1.22207e20			−1.73408			−0.867039	−	0.498240i	$-0.833980\pi$
$443$	−1.22207e20			−1.73408			−0.867039	+	0.498240i	$0.833980\pi$
$444$			2.11502e19i			0.295082i
$445$	−6.50459e19	+	6.50459e19i	−0.892319	+	0.892319i
$446$	4.92753e19			0.664688
$447$	−2.53174e19	+	2.53174e19i	−0.335825	+	0.335825i
$448$	7.92955e18	+	7.92955e18i	0.103434	+	0.103434i
$449$	6.22092e19	+	6.22092e19i	0.798008	+	0.798008i	0.982781	−	0.184773i	$-0.0591550\pi$
$449$	6.22092e19	+	6.22092e19i	0.798008	+	0.798008i	−0.184773	+	0.982781i	$0.559155\pi$
$450$			1.03338e19i			0.130367i
$451$			1.07566e20i			1.33460i
$452$	−1.21547e20	−	1.21547e20i	−1.48323	−	1.48323i
$453$	3.11740e19	+	3.11740e19i	0.374158	+	0.374158i
$454$	−7.75386e19	+	7.75386e19i	−0.915375	+	0.915375i
$455$	−1.67911e19			−0.194981
$456$	1.23465e19	−	1.23465e19i	0.141029	−	0.141029i
$457$		−	9.02995e18i		−	0.101464i	−0.998712	−	0.0507322i	$-0.983844\pi$
$457$		−	9.02995e18i		−	0.101464i	0.998712	−	0.0507322i	$-0.0161555\pi$
$458$	−1.82955e20			−2.02233
$459$	−2.81808e19	+	5.30703e19i	−0.306449	+	0.577107i
$460$	1.72788e20			1.84855
$461$			9.11420e18i			0.0959316i	0.998849	+	0.0479658i	$0.0152738\pi$
$461$			9.11420e18i			0.0959316i	−0.998849	+	0.0479658i	$0.984726\pi$
$462$	4.55375e18	−	4.55375e18i	0.0471579	−	0.0471579i
$463$	−1.10825e20			−1.12922			−0.564610	−	0.825358i	$-0.690973\pi$
$463$	−1.10825e20			−1.12922			−0.564610	+	0.825358i	$0.690973\pi$
$464$	−1.87206e19	+	1.87206e19i	−0.187688	+	0.187688i
$465$	2.24780e19	+	2.24780e19i	0.221749	+	0.221749i
$466$	2.46404e19	+	2.46404e19i	0.239195	+	0.239195i
$467$			1.02885e19i			0.0982819i	0.998792	+	0.0491409i	$0.0156483\pi$
$467$			1.02885e19i			0.0982819i	−0.998792	+	0.0491409i	$0.984352\pi$
$468$			2.30149e20i			2.16354i
$469$	−1.06559e19	−	1.06559e19i	−0.0985811	−	0.0985811i
$470$	−9.97869e19	−	9.97869e19i	−0.908530	−	0.908530i
$471$	−1.87709e19	+	1.87709e19i	−0.168201	+	0.168201i
$472$	3.56946e19			0.314802
$473$	8.93344e19	−	8.93344e19i	0.775461	−	0.775461i
$474$			3.45192e18i			0.0294933i
$475$	1.45347e19			0.122237
$476$	7.26450e18	−	1.36806e19i	0.0601386	−	0.113253i
$477$	−7.33320e19			−0.597593
$478$		−	3.31229e20i		−	2.65717i
$479$	1.12896e20	−	1.12896e20i	0.891581	−	0.891581i	−0.103091	−	0.994672i	$-0.532873\pi$
$479$	1.12896e20	−	1.12896e20i	0.891581	−	0.891581i	0.994672	+	0.103091i	$0.0328732\pi$
$480$	−6.46071e19			−0.502309
$481$	−1.13767e20	+	1.13767e20i	−0.870822	+	0.870822i
$482$	−1.68884e20	−	1.68884e20i	−1.27273	−	1.27273i
$483$	−4.42106e18	−	4.42106e18i	−0.0328037	−	0.0328037i
$484$		−	1.15462e20i		−	0.843525i
$485$			2.19706e20i			1.58044i
$486$	−1.33311e20	−	1.33311e20i	−0.944262	−	0.944262i
$487$	−1.94190e20	−	1.94190e20i	−1.35444	−	1.35444i	−0.880628	−	0.473808i	$-0.842879\pi$
$487$	−1.94190e20	−	1.94190e20i	−1.35444	−	1.35444i	−0.473808	−	0.880628i	$-0.657121\pi$
$488$	4.20560e19	−	4.20560e19i	0.288855	−	0.288855i
$489$	−4.69181e19			−0.317339
$490$	1.67128e20	−	1.67128e20i	1.11321	−	1.11321i
$491$			2.81737e20i			1.84813i	0.382237	+	0.924064i	$0.375154\pi$
$491$			2.81737e20i			1.84813i	−0.382237	+	0.924064i	$0.624846\pi$
$492$	7.28765e19			0.470814
$493$	6.07575e19	+	3.22628e19i	0.386588	+	0.205282i
$494$	5.72287e20			3.58643
$495$		−	1.91541e20i		−	1.18229i
$496$	6.07068e19	−	6.07068e19i	0.369084	−	0.369084i
$497$	1.89568e19			0.113525
$498$	−2.43585e19	+	2.43585e19i	−0.143691	+	0.143691i
$499$	6.61756e19	+	6.61756e19i	0.384542	+	0.384542i	0.872735	−	0.488194i	$-0.162344\pi$
$499$	6.61756e19	+	6.61756e19i	0.384542	+	0.384542i	−0.488194	+	0.872735i	$0.662344\pi$
$500$	−1.52067e20	−	1.52067e20i	−0.870481	−	0.870481i
$501$			1.05445e19i			0.0594623i
$502$			9.32706e19i			0.518164i
$503$	2.39748e20	+	2.39748e20i	1.31219	+	1.31219i	0.919802	+	0.392384i	$0.128349\pi$
$503$	2.39748e20	+	2.39748e20i	1.31219	+	1.31219i	0.392384	+	0.919802i	$0.371651\pi$
$504$	5.20563e18	+	5.20563e18i	0.0280701	+	0.0280701i
$505$	1.45075e20	−	1.45075e20i	0.770741	−	0.770741i
$506$	−5.04126e20			−2.63882
$507$	1.22612e20	−	1.22612e20i	0.632375	−	0.632375i
$508$			1.75786e20i			0.893316i
$509$	−1.84359e20			−0.923170			−0.461585	−	0.887096i	$-0.652719\pi$
$509$	−1.84359e20			−0.923170			−0.461585	+	0.887096i	$0.652719\pi$
$510$	3.28142e19	+	1.07121e20i	0.161914	+	0.528565i
$511$	1.62301e19			0.0789160
$512$			2.32525e20i			1.11415i
$513$	−1.22378e20	+	1.22378e20i	−0.577859	+	0.577859i
$514$	−2.30835e20			−1.07418
$515$	1.73855e20	−	1.73855e20i	0.797322	−	0.797322i
$516$	−6.05243e19	−	6.05243e19i	−0.273563	−	0.273563i
$517$	1.64679e20	+	1.64679e20i	0.733601	+	0.733601i
$518$			2.21742e19i			0.0973586i
$519$		−	8.52345e19i		−	0.368859i
$520$	1.50535e20	+	1.50535e20i	0.642112	+	0.642112i
$521$	1.80903e19	+	1.80903e19i	0.0760612	+	0.0760612i	0.744114	−	0.668053i	$-0.232872\pi$
$521$	1.80903e19	+	1.80903e19i	0.0760612	+	0.0760612i	−0.668053	+	0.744114i	$0.732872\pi$
$522$	−9.96104e19	+	9.96104e19i	−0.412834	+	0.412834i
$523$	−3.60035e20			−1.47090			−0.735449	−	0.677580i	$-0.763029\pi$
$523$	−3.60035e20			−1.47090			−0.735449	+	0.677580i	$0.763029\pi$
$524$	1.89073e20	−	1.89073e20i	0.761457	−	0.761457i
$525$		−	8.42957e17i		−	0.00334665i
$526$	3.17696e20			1.24342
$527$	−1.97023e20	−	1.04621e20i	−0.760217	−	0.403682i
$528$	7.11563e19			0.270682
$529$			2.22801e20i			0.835602i
$530$	−2.06660e20	+	2.06660e20i	−0.764165	+	0.764165i
$531$	−1.65517e20			−0.603439
$532$	3.15468e19	−	3.15468e19i	0.113401	−	0.113401i
$533$	3.92004e20	+	3.92004e20i	1.38943	+	1.38943i
$534$	−1.28575e20	−	1.28575e20i	−0.449362	−	0.449362i
$535$		−	3.29969e20i		−	1.13716i
$536$			1.91064e20i			0.649295i
$537$	3.08909e19	+	3.08909e19i	0.103520	+	0.103520i
$538$	−6.69056e19	−	6.69056e19i	−0.221103	−	0.221103i
$539$	−2.75813e20	+	2.75813e20i	−0.898874	+	0.898874i
$540$	−2.77389e20			−0.891531
$541$	6.58284e19	−	6.58284e19i	0.208657	−	0.208657i	−0.595039	−	0.803697i	$-0.702864\pi$
$541$	6.58284e19	−	6.58284e19i	0.208657	−	0.208657i	0.803697	+	0.595039i	$0.202864\pi$
$542$			5.32939e20i			1.66603i
$543$	−1.22650e20			−0.378153
$544$	4.33498e20	−	1.32793e20i	1.31824	−	0.403815i
$545$	3.28226e20			0.984464
$546$		−	3.31905e19i		−	0.0981903i
$547$	2.29239e20	−	2.29239e20i	0.668933	−	0.668933i	−0.288536	−	0.957469i	$-0.593168\pi$
$547$	2.29239e20	−	2.29239e20i	0.668933	−	0.668933i	0.957469	+	0.288536i	$0.0931684\pi$
$548$	−3.45250e20			−0.993756
$549$	−1.95015e20	+	1.95015e20i	−0.553701	+	0.553701i
$550$	−4.80605e19	−	4.80605e19i	−0.134607	−	0.134607i
$551$	1.40104e20	+	1.40104e20i	0.387092	+	0.387092i
$552$			7.92710e19i			0.216058i
$553$			2.04708e18i			0.00550422i
$554$	3.66552e20	+	3.66552e20i	0.972327	+	0.972327i
$555$	−6.41478e19	−	6.41478e19i	−0.167874	−	0.167874i
$556$	−4.05169e18	+	4.05169e18i	−0.0104611	+	0.0104611i
$557$	3.03079e20			0.772045			0.386022	−	0.922489i	$-0.373849\pi$
$557$	3.03079e20			0.772045			0.386022	+	0.922489i	$0.373849\pi$
$558$	3.23014e20	−	3.23014e20i	0.811831	−	0.811831i
$559$		−	6.51123e20i		−	1.61464i
$560$	−2.55694e19			−0.0625621
$561$	−5.41535e19	−	1.76783e20i	−0.130739	−	0.426795i
$562$	1.60798e20			0.383053
$563$		−	5.13389e20i		−	1.20680i	−0.797440	−	0.603398i	$-0.793813\pi$
$563$		−	5.13389e20i		−	1.20680i	0.797440	−	0.603398i	$-0.206187\pi$
$564$	1.11571e20	−	1.11571e20i	0.258795	−	0.258795i
$565$	7.37297e20			1.68764
$566$	2.03548e20	−	2.03548e20i	0.459773	−	0.459773i
$567$	−2.03616e19	−	2.03616e19i	−0.0453877	−	0.0453877i
$568$	−1.69950e20	−	1.69950e20i	−0.373861	−	0.373861i
$569$			5.54878e20i			1.20464i	0.798256	+	0.602318i	$0.205756\pi$
$569$			5.54878e20i			1.20464i	−0.798256	+	0.602318i	$0.794244\pi$
$570$			3.22685e20i			0.691380i
$571$	−5.20430e20	−	5.20430e20i	−1.10050	−	1.10050i	−0.994350	−	0.106154i	$-0.966146\pi$
$571$	−5.20430e20	−	5.20430e20i	−1.10050	−	1.10050i	−0.106154	−	0.994350i	$-0.533854\pi$
$572$	−1.07038e21	−	1.07038e21i	−2.23392	−	2.23392i
$573$	−2.14927e19	+	2.14927e19i	−0.0442723	+	0.0442723i
$574$	7.64047e19			0.155339
$575$	−4.66601e19	+	4.66601e19i	−0.0936347	+	0.0936347i
$576$			6.59291e20i			1.30589i
$577$	4.00383e20			0.782811			0.391405	−	0.920218i	$-0.371989\pi$
$577$	4.00383e20			0.782811			0.391405	+	0.920218i	$0.371989\pi$
$578$	−4.40350e20	−	6.51311e20i	−0.849845	−	1.25698i
$579$	−6.59301e19			−0.125601
$580$			3.17569e20i			0.597212i
$581$	−1.44452e19	+	1.44452e19i	−0.0268166	+	0.0268166i
$582$	−4.34287e20			−0.795892
$583$	3.41053e20	−	3.41053e20i	0.617032	−	0.617032i
$584$	−1.45506e20	−	1.45506e20i	−0.259887	−	0.259887i
$585$	−6.98033e20	−	6.98033e20i	−1.23086	−	1.23086i
$586$			1.73362e20i			0.301802i
$587$			9.23257e19i			0.158685i	0.996847	+	0.0793427i	$0.0252821\pi$
$587$			9.23257e19i			0.158685i	−0.996847	+	0.0793427i	$0.974718\pi$
$588$	1.86864e20	+	1.86864e20i	0.317099	+	0.317099i
$589$	−4.54327e20	−	4.54327e20i	−0.761208	−	0.761208i
$590$	−4.66450e20	+	4.66450e20i	−0.771640	+	0.771640i
$591$	1.87327e20			0.305981
$592$	−1.73245e20	+	1.73245e20i	−0.279414	+	0.279414i
$593$			1.19941e21i			1.91010i	0.296444	+	0.955050i	$0.404199\pi$
$593$			1.19941e21i			1.91010i	−0.296444	+	0.955050i	$0.595801\pi$
$594$	8.09309e20			1.27267
$595$	1.94597e19	+	6.35256e19i	0.0302175	+	0.0986442i
$596$	1.15989e21			1.77857
$597$			1.22376e20i			0.185305i
$598$	−1.83719e21	+	1.83719e21i	−2.74723	+	2.74723i
$599$	−3.93524e20			−0.581126			−0.290563	−	0.956856i	$-0.593843\pi$
$599$	−3.93524e20			−0.581126			−0.290563	+	0.956856i	$0.593843\pi$
$600$	−7.55725e18	+	7.55725e18i	−0.0110212	+	0.0110212i
$601$	−8.28682e20	−	8.28682e20i	−1.19352	−	1.19352i	−0.976072	−	0.217446i	$-0.930227\pi$
$601$	−8.28682e20	−	8.28682e20i	−1.19352	−	1.19352i	−0.217446	−	0.976072i	$-0.569773\pi$
$602$	−6.34545e19	−	6.34545e19i	−0.0902587	−	0.0902587i
$603$		−	8.85968e20i		−	1.24462i
$604$		−	1.42820e21i		−	1.98159i
$605$	3.50191e20	+	3.50191e20i	0.479888	+	0.479888i
$606$	2.86767e20	+	2.86767e20i	0.388137	+	0.388137i
$607$	−9.09099e20	+	9.09099e20i	−1.21533	+	1.21533i	−0.246087	+	0.969248i	$0.579145\pi$
$607$	−9.09099e20	+	9.09099e20i	−1.21533	+	1.21533i	−0.969248	+	0.246087i	$0.920855\pi$
$608$	1.30584e21			1.72430
$609$	8.12550e18	−	8.12550e18i	0.0105979	−	0.0105979i
$610$			1.09916e21i			1.41608i
$611$	1.20028e21			1.52748
$612$	8.70722e20	−	2.66726e20i	1.09457	−	0.335298i
$613$	−6.34574e20			−0.788004			−0.394002	−	0.919109i	$-0.628910\pi$
$613$	−6.34574e20			−0.788004			−0.394002	+	0.919109i	$0.628910\pi$
$614$		−	7.25179e20i		−	0.889575i
$615$	−2.21032e20	+	2.21032e20i	−0.267850	+	0.267850i
$616$	−4.84207e19			−0.0579664
$617$	−6.33818e20	+	6.33818e20i	−0.749594	+	0.749594i	−0.974403	−	0.224809i	$-0.927824\pi$
$617$	−6.33818e20	+	6.33818e20i	−0.749594	+	0.749594i	0.224809	+	0.974403i	$0.427824\pi$
$618$	3.43655e20	+	3.43655e20i	0.401522	+	0.401522i
$619$	−1.10039e21	−	1.10039e21i	−1.27018	−	1.27018i	−0.945992	−	0.324191i	$-0.894908\pi$
$619$	−1.10039e21	−	1.10039e21i	−1.27018	−	1.27018i	−0.324191	−	0.945992i	$-0.605092\pi$
$620$		−	1.02981e21i		−	1.17441i
$621$		−	7.85726e20i		−	0.885287i
$622$	1.31637e21	+	1.31637e21i	1.46538	+	1.46538i
$623$	−7.62482e19	−	7.62482e19i	−0.0838628	−	0.0838628i
$624$	2.59315e20	−	2.59315e20i	0.281801	−	0.281801i
$625$	1.01345e21			1.08819
$626$	2.99615e19	−	2.99615e19i	0.0317875	−	0.0317875i
$627$		−	5.32530e20i		−	0.558261i
$628$	8.59970e20			0.890812
$629$	5.62265e20	+	2.98568e20i	0.575521	+	0.305607i
$630$	−1.36052e20			−0.137611
$631$			9.27595e20i			0.927125i	0.886064	+	0.463563i	$0.153429\pi$
$631$			9.27595e20i			0.927125i	−0.886064	+	0.463563i	$0.846571\pi$
$632$	1.83524e19	−	1.83524e19i	0.0181265	−	0.0181265i
$633$	−4.44449e20			−0.433805
$634$	−2.41702e20	+	2.41702e20i	−0.233137	+	0.233137i
$635$	−5.33151e20	−	5.33151e20i	−0.508215	−	0.508215i
$636$	−2.31064e20	−	2.31064e20i	−0.217673	−	0.217673i
$637$			2.01029e21i			1.87160i
$638$		−	9.26538e20i		−	0.852527i
$639$	7.88065e20	+	7.88065e20i	0.716648	+	0.716648i
$640$	7.21510e20	+	7.21510e20i	0.648474	+	0.648474i
$641$	5.86136e20	−	5.86136e20i	0.520671	−	0.520671i	−0.397103	−	0.917774i	$-0.629985\pi$
$641$	5.86136e20	−	5.86136e20i	0.520671	−	0.520671i	0.917774	+	0.397103i	$0.129985\pi$
$642$	6.52242e20			0.572659
$643$	−9.11729e20	+	9.11729e20i	−0.791195	+	0.791195i	−0.981688	−	0.190493i	$-0.938991\pi$
$643$	−9.11729e20	+	9.11729e20i	−0.791195	+	0.791195i	0.190493	+	0.981688i	$0.438991\pi$
$644$			2.02546e20i			0.173732i
$645$	3.67136e20			0.311264
$646$	−6.63241e20	−	2.16514e21i	−0.555812	−	1.81443i
$647$	3.47273e20			0.287666			0.143833	−	0.989602i	$-0.454057\pi$
$647$	3.47273e20			0.287666			0.143833	+	0.989602i	$0.454057\pi$
$648$			3.65089e20i			0.298942i
$649$	7.69787e20	−	7.69787e20i	0.623068	−	0.623068i
$650$	−3.50294e20			−0.280274
$651$	−2.63492e19	+	2.63492e19i	−0.0208406	+	0.0208406i
$652$	1.07475e21	+	1.07475e21i	0.840333	+	0.840333i
$653$	−1.09901e21	−	1.09901e21i	−0.849476	−	0.849476i	0.140592	−	0.990068i	$-0.455099\pi$
$653$	−1.09901e21	−	1.09901e21i	−0.849476	−	0.849476i	−0.990068	+	0.140592i	$0.955099\pi$
$654$			6.48797e20i			0.495765i
$655$			1.14691e21i			0.866399i
$656$	5.96945e20	+	5.96945e20i	0.445816	+	0.445816i
$657$	6.74714e20	+	6.74714e20i	0.498173	+	0.498173i
$658$	1.16972e20	−	1.16972e20i	0.0853864	−	0.0853864i
$659$	2.15528e20			0.155547			0.0777737	−	0.996971i	$-0.475219\pi$
$659$	2.15528e20			0.155547			0.0777737	+	0.996971i	$0.475219\pi$
$660$	6.03533e20	−	6.03533e20i	0.430647	−	0.430647i
$661$			1.59871e21i			1.12787i	0.825820	+	0.563933i	$0.190713\pi$
$661$			1.59871e21i			1.12787i	−0.825820	+	0.563933i	$0.809287\pi$
$662$	4.46732e20			0.311610
$663$	−8.41602e20	−	4.46899e20i	−0.580437	−	0.308218i
$664$	2.59008e20			0.176625
$665$			1.91360e20i			0.129030i
$666$	−9.21819e20	+	9.21819e20i	−0.614595	+	0.614595i
$667$	−8.99539e20			−0.593029
$668$	2.41542e20	−	2.41542e20i	0.157460	−	0.157460i
$669$	−1.67099e20	−	1.67099e20i	−0.107715	−	0.107715i
$670$	−2.49678e21	−	2.49678e21i	−1.59155	−	1.59155i
$671$		−	1.81396e21i		−	1.14343i
$672$		−	7.57338e19i		−	0.0472085i
$673$	−5.54128e20	−	5.54128e20i	−0.341584	−	0.341584i	0.515379	−	0.856962i	$-0.327651\pi$
$673$	−5.54128e20	−	5.54128e20i	−0.341584	−	0.341584i	−0.856962	+	0.515379i	$0.827651\pi$
$674$	−1.92482e21	−	1.92482e21i	−1.17338	−	1.17338i
$675$	7.49067e19	−	7.49067e19i	0.0451588	−	0.0451588i
$676$	−5.61736e21			−3.34913
$677$	−1.18896e21	+	1.18896e21i	−0.701054	+	0.701054i	−0.964637	−	0.263583i	$-0.915096\pi$
$677$	−1.18896e21	+	1.18896e21i	−0.701054	+	0.701054i	0.263583	+	0.964637i	$0.415096\pi$
$678$			1.45740e21i			0.849876i
$679$	−2.57543e20			−0.148534
$680$	3.95058e20	−	7.43977e20i	0.225343	−	0.424368i
$681$	5.25886e20			0.296680
$682$			3.00456e21i			1.67648i
$683$	3.80884e20	−	3.80884e20i	0.210202	−	0.210202i	−0.594151	−	0.804353i	$-0.702512\pi$
$683$	3.80884e20	−	3.80884e20i	0.210202	−	0.210202i	0.804353	+	0.594151i	$0.202512\pi$
$684$	2.62291e21			1.43173
$685$	1.04713e21	−	1.04713e21i	0.565356	−	0.565356i
$686$	3.93740e20	+	3.93740e20i	0.210271	+	0.210271i
$687$	6.20422e20	+	6.20422e20i	0.327727	+	0.327727i
$688$		−	9.91531e20i		−	0.518076i
$689$		−	2.48580e21i		−	1.28476i
$690$	−1.03590e21	−	1.03590e21i	−0.529601	−	0.529601i
$691$	8.36942e20	+	8.36942e20i	0.423262	+	0.423262i	0.886325	−	0.463063i	$-0.153250\pi$
$691$	8.36942e20	+	8.36942e20i	0.423262	+	0.423262i	−0.463063	+	0.886325i	$0.653250\pi$
$692$	−1.95246e21	+	1.95246e21i	−0.976759	+	0.976759i
$693$	2.24528e20			0.111115
$694$	1.93296e21	−	1.93296e21i	0.946294	−	0.946294i
$695$		−	2.45773e19i		−	0.0119028i
$696$	−1.45693e20			−0.0698022
$697$	1.02876e21	−	1.93738e21i	0.487607	−	0.918265i
$698$	−4.40954e21			−2.06765
$699$		−	1.67117e20i		−	0.0775251i
$700$	−1.93096e19	+	1.93096e19i	−0.00886213	+	0.00886213i
$701$	1.07040e21			0.486029			0.243015	−	0.970023i	$-0.421864\pi$
$701$	1.07040e21			0.486029			0.243015	+	0.970023i	$0.421864\pi$
$702$	2.94937e21	−	2.94937e21i	1.32495	−	1.32495i
$703$	1.29656e21	+	1.29656e21i	0.576271	+	0.576271i
$704$	−3.06623e21	−	3.06623e21i	−1.34837	−	1.34837i
$705$			6.76779e20i			0.294462i
$706$			3.00463e21i			1.29347i
$707$	1.70060e20	+	1.70060e20i	0.0724365	+	0.0724365i
$708$	−5.21533e20	−	5.21533e20i	−0.219802	−	0.219802i
$709$	5.05219e20	−	5.05219e20i	0.210685	−	0.210685i	−0.593874	−	0.804558i	$-0.702402\pi$
$709$	5.05219e20	−	5.05219e20i	0.210685	−	0.210685i	0.804558	+	0.593874i	$0.202402\pi$
$710$	4.44176e21			1.83281
$711$	−8.51006e19	+	8.51006e19i	−0.0347465	+	0.0347465i
$712$			1.36716e21i			0.552355i
$713$	2.91701e21			1.16618
$714$	−1.25570e20	+	3.84654e19i	−0.0496761	+	0.0152172i
$715$	6.49284e21			2.54179
$716$		−	1.41523e21i		−	0.548252i
$717$	−1.12324e21	+	1.12324e21i	−0.430605	+	0.430605i
$718$	−4.37092e21			−1.65821
$719$	−2.48253e21	+	2.48253e21i	−0.932026	+	0.932026i	−0.997832	−	0.0658065i	$-0.979038\pi$
$719$	−2.48253e21	+	2.48253e21i	−0.932026	+	0.932026i	0.0658065	+	0.997832i	$0.479038\pi$
$720$	−1.06297e21	−	1.06297e21i	−0.394935	−	0.394935i
$721$	2.03797e20	+	2.03797e20i	0.0749347	+	0.0749347i
$722$		−	2.35242e21i		−	0.856023i
$723$			1.14541e21i			0.412501i
$724$	2.80953e21	+	2.80953e21i	1.00137	+	1.00137i
$725$	−8.57570e19	−	8.57570e19i	−0.0302506	−	0.0302506i
$726$	−6.92215e20	+	6.92215e20i	−0.241667	+	0.241667i
$727$	−3.36549e20			−0.116289			−0.0581447	−	0.998308i	$-0.518518\pi$
$727$	−3.36549e20			−0.116289			−0.0581447	+	0.998308i	$0.518518\pi$
$728$	−1.76460e20	+	1.76460e20i	−0.0603476	+	0.0603476i
$729$		−	1.02165e21i		−	0.345818i
$730$	3.80288e21			1.27406
$731$	−2.46339e21	+	7.54606e20i	−0.816871	+	0.250230i
$732$	−1.22896e21			−0.403371
$733$		−	5.34712e21i		−	1.73716i	−0.495549	−	0.868580i	$-0.665033\pi$
$733$		−	5.34712e21i		−	1.73716i	0.495549	−	0.868580i	$-0.334967\pi$
$734$	2.93058e21	−	2.93058e21i	0.942397	−	0.942397i
$735$	−1.13350e21			−0.360801
$736$	−4.19208e21	+	4.19208e21i	−1.32083	+	1.32083i
$737$	4.12047e21	+	4.12047e21i	1.28511	+	1.28511i
$738$	3.17628e21	+	3.17628e21i	0.980609	+	0.980609i
$739$		−	4.46390e21i		−	1.36421i	−0.731254	−	0.682105i	$-0.761065\pi$
$739$		−	4.46390e21i		−	1.36421i	0.731254	−	0.682105i	$-0.238935\pi$
$740$			2.93886e21i			0.889081i
$741$	−1.94070e21	−	1.94070e21i	−0.581194	−	0.581194i
$742$	−2.42251e20	−	2.42251e20i	−0.0718185	−	0.0718185i
$743$	−3.18911e21	+	3.18911e21i	−0.935953	+	0.935953i	−0.998069	−	0.0621160i	$-0.980215\pi$
$743$	−3.18911e21	+	3.18911e21i	−0.935953	+	0.935953i	0.0621160	+	0.998069i	$0.480215\pi$
$744$	4.72450e20			0.137265
$745$	−3.51790e21	+	3.51790e21i	−1.01184	+	1.01184i
$746$		−	2.03922e21i		−	0.580662i
$747$	−1.20103e21			−0.338570
$748$	−2.80907e21	+	5.29006e21i	−0.783972	+	1.47638i
$749$	3.86797e20			0.106873
$750$			1.82334e21i			0.498778i
$751$	8.49251e20	−	8.49251e20i	0.230005	−	0.230005i	−0.582690	−	0.812695i	$-0.698000\pi$
$751$	8.49251e20	−	8.49251e20i	0.230005	−	0.230005i	0.812695	+	0.582690i	$0.198000\pi$
$752$	1.82779e21			0.490109
$753$	3.16292e20	−	3.16292e20i	0.0839704	−	0.0839704i
$754$	−3.37658e21	−	3.37658e21i	−0.887549	−	0.887549i
$755$	4.33169e21	+	4.33169e21i	1.12734	+	1.12734i
$756$		−	3.25162e20i		−	0.0837887i
$757$			3.42802e21i			0.874629i	0.899309	+	0.437315i	$0.144070\pi$
$757$			3.42802e21i			0.874629i	−0.899309	+	0.437315i	$0.855930\pi$
$758$	−2.14999e21	−	2.14999e21i	−0.543147	−	0.543147i
$759$	1.70955e21	+	1.70955e21i	0.427631	+	0.427631i
$760$	1.71558e21	−	1.71558e21i	0.424921	−	0.424921i
$761$	−2.64257e21			−0.648100			−0.324050	−	0.946040i	$-0.605045\pi$
$761$	−2.64257e21			−0.648100			−0.324050	+	0.946040i	$0.605045\pi$
$762$	1.05387e21	−	1.05387e21i	0.255931	−	0.255931i
$763$			3.84754e20i			0.0925228i
$764$	9.84667e20			0.234471
$765$	−1.83190e21	+	3.44984e21i	−0.431957	+	0.813464i
$766$	1.51484e21			0.353714
$767$		−	5.61067e21i		−	1.29733i
$768$	1.69041e20	−	1.69041e20i	0.0387065	−	0.0387065i
$769$	2.81602e21			0.638540			0.319270	−	0.947664i	$-0.396562\pi$
$769$	2.81602e21			0.638540			0.319270	+	0.947664i	$0.396562\pi$
$770$	6.32753e20	−	6.32753e20i	0.142087	−	0.142087i
$771$	7.82791e20	+	7.82791e20i	0.174076	+	0.174076i
$772$	1.51026e21	+	1.51026e21i	0.332600	+	0.332600i
$773$			7.92370e21i			1.72815i	0.503361	+	0.864076i	$0.332097\pi$
$773$			7.92370e21i			1.72815i	−0.503361	+	0.864076i	$0.667903\pi$
$774$		−	5.27583e21i		−	1.13955i
$775$	2.78091e20	+	2.78091e20i	0.0594873	+	0.0594873i
$776$	2.30892e21	+	2.30892e21i	0.489154	+	0.489154i
$777$	7.51954e19	−	7.51954e19i	0.0157773	−	0.0157773i
$778$	−9.73732e21			−2.02345
$779$	4.46750e21	−	4.46750e21i	0.919462	−	0.919462i
$780$		−	4.39891e21i		−	0.896677i
$781$	−7.33028e21			−1.47992
$782$	9.07980e21	+	4.82146e21i	1.81562	+	0.964113i
$783$	1.44409e21			0.286011
$784$			3.06127e21i			0.600526i
$785$	−2.60826e21	+	2.60826e21i	−0.506790	+	0.506790i
$786$	−2.26706e21			−0.436309
$787$	4.10623e21	−	4.10623e21i	0.782768	−	0.782768i	−0.197529	−	0.980297i	$-0.563292\pi$
$787$	4.10623e21	−	4.10623e21i	0.782768	−	0.782768i	0.980297	+	0.197529i	$0.0632916\pi$
$788$	−4.29109e21	−	4.29109e21i	−0.810254	−	0.810254i
$789$	−1.07735e21	−	1.07735e21i	−0.201501	−	0.201501i
$790$			4.79651e20i			0.0888633i
$791$			8.64275e20i			0.158609i
$792$	−2.01293e21	−	2.01293e21i	−0.365924	−	0.365924i
$793$	−6.61060e21	−	6.61060e21i	−1.19040	−	1.19040i
$794$	8.78509e21	−	8.78509e21i	1.56708	−	1.56708i
$795$	1.40162e21			0.247672
$796$	2.80325e21	−	2.80325e21i	0.490698	−	0.490698i
$797$		−	2.76086e21i		−	0.478748i	−0.970927	−	0.239374i	$-0.923058\pi$
$797$		−	2.76086e21i		−	0.478748i	0.970927	−	0.239374i	$-0.0769422\pi$
$798$	−3.78258e20			−0.0649779
$799$	−1.39104e21	−	4.54103e21i	−0.236723	−	0.772775i
$800$	−7.99299e20			−0.134752
$801$		−	6.33954e21i		−	1.05880i
$802$	3.20947e21	−	3.20947e21i	0.531038	−	0.531038i
$803$	−6.27594e21			−1.02875
$804$	2.79163e21	−	2.79163e21i	0.453354	−	0.453354i
$805$	−6.14315e20	−	6.14315e20i	−0.0988376	−	0.0988376i
$806$	1.09495e22	+	1.09495e22i	1.74535	+	1.74535i
$807$			4.53771e20i			0.0716613i
$808$		−	3.04924e21i		−	0.477096i
$809$	−1.28640e21	−	1.28640e21i	−0.199416	−	0.199416i	0.600333	−	0.799750i	$-0.295035\pi$
$809$	−1.28640e21	−	1.28640e21i	−0.199416	−	0.199416i	−0.799750	+	0.600333i	$0.795035\pi$
$810$	−4.77092e21	−	4.77092e21i	−0.732765	−	0.732765i
$811$	−4.49286e21	+	4.49286e21i	−0.683701	+	0.683701i	−0.960832	−	0.277131i	$-0.910616\pi$
$811$	−4.49286e21	+	4.49286e21i	−0.683701	+	0.683701i	0.277131	+	0.960832i	$0.410616\pi$
$812$	−3.72261e20			−0.0561278
$813$	1.80726e21	−	1.80726e21i	0.269987	−	0.269987i
$814$		−	8.57441e21i		−	1.26917i
$815$	−6.51937e21			−0.956144
$816$	−1.28159e21	−	6.80538e20i	−0.186241	−	0.0988955i
$817$	−7.42057e21			−1.06849
$818$			1.56221e22i			2.22890i
$819$	8.18249e20	−	8.18249e20i	0.115679	−	0.115679i
$820$	1.01263e22			1.41856
$821$	−4.92089e21	+	4.92089e21i	−0.683077	+	0.683077i	−0.960692	−	0.277615i	$-0.910456\pi$
$821$	−4.92089e21	+	4.92089e21i	−0.683077	+	0.683077i	0.277615	+	0.960692i	$0.410456\pi$
$822$	2.06984e21	+	2.06984e21i	0.284707	+	0.284707i
$823$	5.65087e21	+	5.65087e21i	0.770223	+	0.770223i	0.978145	−	0.207922i	$-0.0666700\pi$
$823$	5.65087e21	+	5.65087e21i	0.770223	+	0.770223i	−0.207922	+	0.978145i	$0.566670\pi$
$824$		−	3.65414e21i		−	0.493550i
$825$			3.25959e20i			0.0436272i
$826$	−5.46782e20	−	5.46782e20i	−0.0725211	−	0.0725211i
$827$	−5.25820e20	−	5.25820e20i	−0.0691108	−	0.0691108i	0.671707	−	0.740817i	$-0.265562\pi$
$827$	−5.25820e20	−	5.25820e20i	−0.0691108	−	0.0691108i	−0.740817	+	0.671707i	$0.765562\pi$
$828$	−8.42019e21	+	8.42019e21i	−1.09672	+	1.09672i
$829$	3.10552e21			0.400844			0.200422	−	0.979710i	$-0.435769\pi$
$829$	3.10552e21			0.400844			0.200422	+	0.979710i	$0.435769\pi$
$830$	−3.38467e21	+	3.38467e21i	−0.432942	+	0.432942i
$831$		−	2.48605e21i		−	0.315139i
$832$	−2.23486e22			−2.80753
$833$	7.60553e21	−	2.32979e21i	0.946874	−	0.290054i
$834$	4.85813e19			0.00599410
$835$			1.46518e21i			0.179160i
$836$	−1.21986e22	+	1.21986e22i	−1.47831	+	1.47831i
$837$	−4.68288e21			−0.562434
$838$	2.70566e21	−	2.70566e21i	0.322064	−	0.322064i
$839$	9.92909e21	+	9.92909e21i	1.17137	+	1.17137i	0.981883	+	0.189488i	$0.0606829\pi$
$839$	9.92909e21	+	9.92909e21i	1.17137	+	1.17137i	0.189488	+	0.981883i	$0.439317\pi$
$840$	−9.94969e19	−	9.94969e19i	−0.0116336	−	0.0116336i
$841$			6.97592e21i			0.808409i
$842$			4.79324e21i			0.550540i
$843$	−5.45287e20	−	5.45287e20i	−0.0620752	−	0.0620752i
$844$	1.01810e22	+	1.01810e22i	1.14874	+	1.14874i
$845$	1.70373e22	−	1.70373e22i	1.90535	−	1.90535i
$846$	9.72548e21			1.07804
$847$	−4.10502e20	+	4.10502e20i	−0.0451013	+	0.0451013i
$848$		−	3.78538e21i		−	0.412231i
$849$	−1.38051e21			−0.149016
$850$	4.05966e20	+	1.32527e21i	0.0434358	+	0.141795i
$851$	−8.32455e21			−0.882855
$852$			4.96628e21i			0.522077i
$853$	8.78867e21	−	8.78867e21i	0.915811	−	0.915811i	−0.0809108	−	0.996721i	$-0.525783\pi$
$853$	8.78867e21	−	8.78867e21i	0.915811	−	0.915811i	0.996721	+	0.0809108i	$0.0257829\pi$
$854$	−1.28846e21			−0.133087
$855$	−7.95518e21	+	7.95518e21i	−0.814525	+	0.814525i
$856$	−3.46770e21	−	3.46770e21i	−0.351956	−	0.351956i
$857$	−7.23506e21	−	7.23506e21i	−0.727924	−	0.727924i	0.242282	−	0.970206i	$-0.422104\pi$
$857$	−7.23506e21	−	7.23506e21i	−0.727924	−	0.727924i	−0.970206	+	0.242282i	$0.922104\pi$
$858$			1.28342e22i			1.28002i
$859$			4.93113e21i			0.487526i	0.969835	+	0.243763i	$0.0783818\pi$
$859$			4.93113e21i			0.487526i	−0.969835	+	0.243763i	$0.921618\pi$
$860$	−8.40997e21	−	8.40997e21i	−0.824245	−	0.824245i
$861$	−2.59098e20	−	2.59098e20i	−0.0251733	−	0.0251733i
$862$	1.45902e22	−	1.45902e22i	1.40526	−	1.40526i
$863$	−1.01509e22			−0.969225			−0.484612	−	0.874729i	$-0.661039\pi$
$863$	−1.01509e22			−0.969225			−0.484612	+	0.874729i	$0.661039\pi$
$864$	6.72984e21	−	6.72984e21i	0.637018	−	0.637018i
$865$		−	1.18435e22i		−	1.11137i
$866$	−1.46220e22			−1.36026
$867$	−7.15394e20	+	3.70196e21i	−0.0659784	+	0.341420i
$868$	1.20716e21			0.110374
$869$		−	7.91573e20i		−	0.0717534i
$870$	1.90389e21	−	1.90389e21i	0.171099	−	0.171099i
$871$	3.00325e22			2.67581
$872$	3.44938e21	−	3.44938e21i	0.304697	−	0.304697i
$873$	−1.07065e22	−	1.07065e22i	−0.937652	−	0.937652i
$874$	2.09376e22	+	2.09376e22i	1.81799	+	1.81799i
$875$			1.08129e21i			0.0930852i
$876$			4.25196e21i			0.362918i
$877$	−2.82465e21	−	2.82465e21i	−0.239039	−	0.239039i	0.577413	−	0.816452i	$-0.304062\pi$
$877$	−2.82465e21	−	2.82465e21i	−0.239039	−	0.239039i	−0.816452	+	0.577413i	$0.804062\pi$
$878$	2.24280e22	+	2.24280e22i	1.88183	+	1.88183i
$879$	5.87892e20	−	5.87892e20i	0.0489081	−	0.0489081i
$880$	9.88731e21			0.815564
$881$	−1.53309e21	+	1.53309e21i	−0.125386	+	0.125386i	−0.767015	−	0.641629i	$-0.778259\pi$
$881$	−1.53309e21	+	1.53309e21i	−0.125386	+	0.125386i	0.641629	+	0.767015i	$0.278259\pi$
$882$			1.62887e22i			1.32091i
$883$	−4.84260e21			−0.389380			−0.194690	−	0.980865i	$-0.562370\pi$
$883$	−4.84260e21			−0.389380			−0.194690	+	0.980865i	$0.562370\pi$
$884$	9.04147e21	+	2.95157e22i	0.720853	+	2.35321i
$885$	3.16358e21			0.250095
$886$		−	3.35658e22i		−	2.63114i
$887$	1.46213e22	−	1.46213e22i	1.13648	−	1.13648i	0.147398	−	0.989077i	$-0.452910\pi$
$887$	1.46213e22	−	1.46213e22i	1.13648	−	1.13648i	0.989077	−	0.147398i	$-0.0470898\pi$
$888$	−1.34828e21			−0.103916
$889$	6.24971e20	−	6.24971e20i	0.0477636	−	0.0477636i
$890$	−1.78657e22	−	1.78657e22i	−1.35393	−	1.35393i
$891$	7.87350e21	+	7.87350e21i	0.591677	+	0.591677i
$892$			7.65545e21i			0.570472i
$893$		−	1.36791e22i		−	1.01081i
$894$	−6.95376e21	−	6.95376e21i	−0.509552	−	0.509552i
$895$	4.29235e21	+	4.29235e21i	0.311905	+	0.311905i
$896$	−8.45769e20	+	8.45769e20i	−0.0609455	+	0.0609455i
$897$	1.24603e22			0.890397
$898$	−1.70866e22	+	1.70866e22i	−1.21083	+	1.21083i
$899$			5.36119e21i			0.376759i
$900$	−1.60547e21			−0.111888
$901$	−9.40453e21	+	2.88087e21i	−0.649982	+	0.199107i
$902$	−2.95445e22			−2.02501
$903$			4.30364e20i			0.0292535i
$904$	7.74837e21	−	7.74837e21i	0.522333	−	0.522333i
$905$	−1.70424e22			−1.13938
$906$	−8.56234e21	+	8.56234e21i	−0.567716	+	0.567716i
$907$	−1.02222e22	−	1.02222e22i	−0.672189	−	0.672189i	0.286031	−	0.958220i	$-0.407664\pi$
$907$	−1.02222e22	−	1.02222e22i	−0.672189	−	0.672189i	−0.958220	+	0.286031i	$0.907664\pi$
$908$	−1.20465e22	−	1.20465e22i	−0.785625	−	0.785625i
$909$			1.41394e22i			0.914539i
$910$		−	4.61188e21i		−	0.295848i
$911$	3.22396e21	+	3.22396e21i	0.205117	+	0.205117i	0.802188	−	0.597071i	$-0.203669\pi$
$911$	3.22396e21	+	3.22396e21i	0.205117	+	0.205117i	−0.597071	+	0.802188i	$0.703669\pi$
$912$	−2.95530e21	−	2.95530e21i	−0.186483	−	0.186483i
$913$	5.58575e21	−	5.58575e21i	0.349583	−	0.349583i
$914$	2.48020e21			0.153953
$915$	3.72739e21	−	3.72739e21i	0.229481	−	0.229481i
$916$		−	2.84240e22i		−	1.73568i
$917$	−1.34443e21			−0.0814267
$918$	−1.45764e22	−	7.74023e21i	−0.875652	−	0.464979i
$919$	1.57678e22			0.939520			0.469760	−	0.882794i	$-0.344341\pi$
$919$	1.57678e22			0.939520			0.469760	+	0.882794i	$0.344341\pi$
$920$			1.10149e22i			0.650985i
$921$	−2.45917e21	+	2.45917e21i	−0.144159	+	0.144159i
$922$	−2.50334e21			−0.145558
$923$	−2.67138e22	+	2.67138e22i	−1.54071	+	1.54071i
$924$	7.07474e20	+	7.07474e20i	0.0404735	+	0.0404735i
$925$	−7.93616e20	−	7.93616e20i	−0.0450347	−	0.0450347i
$926$		−	3.04394e22i		−	1.71338i
$927$			1.69444e22i			0.946079i
$928$	−7.70466e21	−	7.70466e21i	−0.426721	−	0.426721i
$929$	−1.28714e22	−	1.28714e22i	−0.707144	−	0.707144i	0.258790	−	0.965934i	$-0.416676\pi$
$929$	−1.28714e22	−	1.28714e22i	−0.707144	−	0.707144i	−0.965934	+	0.258790i	$0.916676\pi$
$930$	−6.17389e21	+	6.17389e21i	−0.336462	+	0.336462i
$931$	2.29104e22			1.23854
$932$	−3.82815e21	+	3.82815e21i	−0.205291	+	0.205291i
$933$		−	8.92793e21i		−	0.474939i
$934$	−2.82586e21			−0.149125
$935$	−7.52475e21	−	2.45644e22i	−0.393917	−	1.28593i
$936$	−1.46715e22			−0.761912
$937$			1.17201e21i			0.0603789i	0.999544	+	0.0301894i	$0.00961105\pi$
$937$			1.17201e21i			0.0603789i	−0.999544	+	0.0301894i	$0.990389\pi$
$938$	2.92678e21	−	2.92678e21i	0.149579	−	0.149579i
$939$	−2.03207e20			−0.0103026
$940$	1.55030e22	−	1.55030e22i	0.779751	−	0.779751i
$941$	1.02726e22	+	1.02726e22i	0.512578	+	0.512578i	0.915316	−	0.402737i	$-0.131941\pi$
$941$	1.02726e22	+	1.02726e22i	0.512578	+	0.512578i	−0.402737	+	0.915316i	$0.631941\pi$
$942$	−5.15568e21	−	5.15568e21i	−0.255214	−	0.255214i
$943$			2.86836e22i			1.40863i
$944$		−	8.54394e21i		−	0.416264i
$945$	9.86203e20	+	9.86203e20i	0.0476681	+	0.0476681i
$946$	2.45369e22	+	2.45369e22i	1.17662	+	1.17662i
$947$	−5.14196e21	+	5.14196e21i	−0.244627	+	0.244627i	−0.818761	−	0.574134i	$-0.805339\pi$
$947$	−5.14196e21	+	5.14196e21i	−0.244627	+	0.244627i	0.574134	+	0.818761i	$0.305339\pi$
$948$	−5.36293e20			−0.0253128
$949$	−2.28714e22	+	2.28714e22i	−1.07102	+	1.07102i
$950$			3.99215e21i			0.185473i
$951$	1.63928e21			0.0755613
$952$	8.72105e20	+	4.63096e20i	0.0398833	+	0.0211784i
$953$	1.17065e22			0.531165			0.265582	−	0.964088i	$-0.414436\pi$
$953$	1.17065e22			0.531165			0.265582	+	0.964088i	$0.414436\pi$
$954$		−	2.01416e22i		−	0.906736i
$955$	−2.98646e21	+	2.98646e21i	−0.133392	+	0.133392i
$956$	5.14600e22			2.28053
$957$	−3.14201e21	+	3.14201e21i	−0.138155	+	0.138155i
$958$	3.10083e22	+	3.10083e22i	1.35281	+	1.35281i
$959$	1.22747e21	+	1.22747e21i	0.0531338	+	0.0531338i
$960$		−	1.26012e22i		−	0.541227i
$961$			6.08010e21i			0.259111i
$962$	−3.12477e22	−	3.12477e22i	−1.32131	−	1.32131i
$963$	1.60798e22	+	1.60798e22i	0.674658	+	0.674658i
$964$	2.62380e22	−	2.62380e22i	1.09233	−	1.09233i
$965$	−9.16113e21			−0.378438
$966$	1.21430e21	−	1.21430e21i	0.0497735	−	0.0497735i
$967$		−	2.48763e22i		−	1.01178i	−0.862597	−	0.505892i	$-0.831163\pi$
$967$		−	2.48763e22i		−	1.01178i	0.862597	−	0.505892i	$-0.168837\pi$
$968$	7.36043e21			0.297056
$969$	−5.09311e21	+	9.59138e21i	−0.203965	+	0.384107i
$970$	−6.03450e22			−2.39802
$971$		−	3.19214e20i		−	0.0125874i	−0.999980	−	0.00629372i	$-0.997997\pi$
$971$		−	3.19214e20i		−	0.0125874i	0.999980	−	0.00629372i	$-0.00200337\pi$
$972$	2.07112e22	−	2.07112e22i	0.810418	−	0.810418i
$973$	2.88100e19			0.00111866
$974$	5.33367e22	−	5.33367e22i	2.05511	−	2.05511i
$975$	1.18789e21	+	1.18789e21i	0.0454195	+	0.0454195i
$976$	−1.00666e22	−	1.00666e22i	−0.381954	−	0.381954i
$977$		−	2.94533e22i		−	1.10898i	−0.832190	−	0.554491i	$-0.812913\pi$
$977$		−	2.94533e22i		−	1.10898i	0.832190	−	0.554491i	$-0.187087\pi$
$978$		−	1.28867e22i		−	0.481504i
$979$	2.94840e22	+	2.94840e22i	1.09324	+	1.09324i
$980$	2.59651e22	+	2.59651e22i	0.955421	+	0.955421i
$981$	−1.59949e22	+	1.59949e22i	−0.584068	+	0.584068i
$982$	−7.73827e22			−2.80419
$983$	−2.27587e22	+	2.27587e22i	−0.818457	+	0.818457i	−0.985884	−	0.167428i	$-0.946454\pi$
$983$	−2.27587e22	+	2.27587e22i	−0.818457	+	0.818457i	0.167428	+	0.985884i	$0.446454\pi$
$984$			4.64571e21i			0.165802i
$985$	2.60295e22			0.921920
$986$	−8.86140e21	+	1.66879e22i	−0.311477	+	0.586575i
$987$	−7.93335e20			−0.0276744
$988$			8.89110e22i			3.07807i
$989$	2.38219e22	−	2.38219e22i	0.818472	−	0.818472i
$990$	5.26093e22			1.79390
$991$	1.29210e22	−	1.29210e22i	0.437263	−	0.437263i	−0.453827	−	0.891090i	$-0.649941\pi$
$991$	1.29210e22	−	1.29210e22i	0.437263	−	0.437263i	0.891090	+	0.453827i	$0.149941\pi$
$992$	2.49845e22	+	2.49845e22i	0.839138	+	0.839138i
$993$	−1.51492e21	−	1.51492e21i	−0.0504976	−	0.0504976i
$994$			5.20672e21i			0.172253i
$995$			1.70043e22i			0.558324i
$996$	−3.78436e21	−	3.78436e21i	−0.123324	−	0.123324i
$997$	−3.24536e22	−	3.24536e22i	−1.04966	−	1.04966i	−0.998701	−	0.0509594i	$-0.983772\pi$
$997$	−3.24536e22	−	3.24536e22i	−1.04966	−	1.04966i	−0.0509594	−	0.998701i	$-0.516228\pi$
$998$	−1.81760e22	+	1.81760e22i	−0.583471	+	0.583471i
$999$	1.33640e22			0.425790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.16.c.a.4.19	✓	44
17.13	even	4	inner	17.16.c.a.13.4	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.16.c.a.4.19	✓	44	1.1	even	1	trivial
17.16.c.a.13.4	yes	44	17.13	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:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+274.663i q^{2} +(931.417 - 931.417i) q^{3} -42671.9 q^{4} +(129422. - 129422. i) q^{5} +(255826. + 255826. i) q^{6} +(151712. + 151712. i) q^{7} -2.72024e6i q^{8} +1.26138e7i q^{9} +O(q^{10})\)	\(q+274.663i q^{2} +(931.417 - 931.417i) q^{3} -42671.9 q^{4} +(129422. - 129422. i) q^{5} +(255826. + 255826. i) q^{6} +(151712. + 151712. i) q^{7} -2.72024e6i q^{8} +1.26138e7i q^{9} +(3.55476e7 + 3.55476e7i) q^{10} +(-5.86645e7 - 5.86645e7i) q^{11} +(-3.97454e7 + 3.97454e7i) q^{12} -4.27582e8 q^{13} +(-4.16696e7 + 4.16696e7i) q^{14} -2.41092e8i q^{15} -6.51123e8 q^{16} +(4.95538e8 + 1.61767e9i) q^{17} -3.46456e9 q^{18} +4.87297e9i q^{19} +(-5.52270e9 + 5.52270e9i) q^{20} +2.82614e8 q^{21} +(1.61130e10 - 1.61130e10i) q^{22} +(-1.56435e10 - 1.56435e10i) q^{23} +(-2.53368e9 - 2.53368e9i) q^{24} -2.98272e9i q^{25} -1.17441e11i q^{26} +(2.51136e10 + 2.51136e10i) q^{27} +(-6.47382e9 - 6.47382e9i) q^{28} +(2.87513e10 - 2.87513e10i) q^{29} +6.62192e10 q^{30} +(-9.32340e10 + 9.32340e10i) q^{31} -2.67976e11i q^{32} -1.09282e11 q^{33} +(-4.44315e11 + 1.36106e11i) q^{34} +3.92698e10 q^{35} -5.38256e11i q^{36} +(2.66071e11 - 2.66071e11i) q^{37} -1.33843e12 q^{38} +(-3.98258e11 + 3.98258e11i) q^{39} +(-3.52060e11 - 3.52060e11i) q^{40} +(-9.16792e11 - 9.16792e11i) q^{41} +7.76236e10i q^{42} +1.52280e12i q^{43} +(2.50333e12 + 2.50333e12i) q^{44} +(1.63251e12 + 1.63251e12i) q^{45} +(4.29669e12 - 4.29669e12i) q^{46} -2.80714e12 q^{47} +(-6.06468e11 + 6.06468e11i) q^{48} -4.70153e12i q^{49} +8.19244e11 q^{50} +(1.96828e12 + 1.04518e12i) q^{51} +1.82458e13 q^{52} +5.81362e12i q^{53} +(-6.89777e12 + 6.89777e12i) q^{54} -1.51850e13 q^{55} +(4.12692e11 - 4.12692e11i) q^{56} +(4.53877e12 + 4.53877e12i) q^{57} +(7.89692e12 + 7.89692e12i) q^{58} +1.31219e13i q^{59} +1.02879e13i q^{60} +(1.54604e13 + 1.54604e13i) q^{61} +(-2.56080e13 - 2.56080e13i) q^{62} +(-1.91366e12 + 1.91366e12i) q^{63} +5.22673e13 q^{64} +(-5.53387e13 + 5.53387e13i) q^{65} -3.00158e13i q^{66} -7.02378e13 q^{67} +(-2.11456e13 - 6.90292e13i) q^{68} -2.91412e13 q^{69} +1.07860e13i q^{70} +(6.24763e13 - 6.24763e13i) q^{71} +3.43126e13 q^{72} +(5.34901e13 - 5.34901e13i) q^{73} +(7.30800e13 + 7.30800e13i) q^{74} +(-2.77816e12 - 2.77816e12i) q^{75} -2.07939e14i q^{76} -1.78002e13i q^{77} +(-1.09387e14 - 1.09387e14i) q^{78} +(6.74661e12 + 6.74661e12i) q^{79} +(-8.42699e13 + 8.42699e13i) q^{80} -1.34212e14 q^{81} +(2.51809e14 - 2.51809e14i) q^{82} +9.52151e13i q^{83} -1.20597e13 q^{84} +(2.73497e14 + 1.45229e14i) q^{85} -4.18258e14 q^{86} -5.35589e13i q^{87} +(-1.59582e14 + 1.59582e14i) q^{88} -5.02587e14 q^{89} +(-4.48391e14 + 4.48391e14i) q^{90} +(-6.48692e13 - 6.48692e13i) q^{91} +(6.67537e14 + 6.67537e14i) q^{92} +1.73680e14i q^{93} -7.71017e14i q^{94} +(6.30672e14 + 6.30672e14i) q^{95} +(-2.49598e14 - 2.49598e14i) q^{96} +(-8.48793e14 + 8.48793e14i) q^{97} +1.29134e15 q^{98} +(7.39984e14 - 7.39984e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7}+O(q^{10}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7	\( 44 q + 5256 q^{3} - 720900 q^{4} - 252126 q^{5} - 1017326 q^{6} + 1854722 q^{7} + 8409498 q^{10} - 9729300 q^{11} - 82056486 q^{12} + 146863304 q^{13} - 1773752796 q^{14} + 16082152452 q^{16} + 1961077578 q^{17} - 7034899972 q^{18} + 21230427174 q^{20} - 47057263940 q^{21} - 3442343910 q^{22} - 15842736534 q^{23} + 94553484290 q^{24} - 294640558020 q^{27} - 17774164556 q^{28} + 102726169530 q^{29} - 643189839240 q^{30} - 385043642942 q^{31} + 2378676720192 q^{33} + 158249007174 q^{34} + 408521183892 q^{35} + 1375134180422 q^{37} + 1543745804832 q^{38} + 603440813444 q^{39} - 8303553806742 q^{40} + 1443758220300 q^{41} - 4657636435362 q^{44} + 6106558559866 q^{45} + 9604057332832 q^{46} - 21302607302640 q^{47} + 25515630744334 q^{48} - 18255254395212 q^{50} + 19158460873088 q^{51} - 48159060495244 q^{52} - 78998282739512 q^{54} + 13393057779764 q^{55} + 137860752160332 q^{56} + 31257866131908 q^{57} - 69211880377042 q^{58} + 38643830633662 q^{61} + 238390785941076 q^{62} - 71567394446902 q^{63} - 498262566925124 q^{64} + 178535375770548 q^{65} + 57983772499388 q^{67} + 261849713539554 q^{68} - 115652283503244 q^{69} - 44377197355566 q^{71} + 93677094320796 q^{72} + 405163878377696 q^{73} - 405068893451898 q^{74} + 225803653508132 q^{75} - 802546741257484 q^{78} - 155549526248110 q^{79} - 124920621818622 q^{80} - 10\!\cdots\!28 q^{81}+ \cdots + 173739293641872 q^{99}+O(q^{100}) \) 44 * q + 5256 * q^3 - 720900 * q^4 - 252126 * q^5 - 1017326 * q^6 + 1854722 * q^7 + 8409498 * q^10 - 9729300 * q^11 - 82056486 * q^12 + 146863304 * q^13 - 1773752796 * q^14 + 16082152452 * q^16 + 1961077578 * q^17 - 7034899972 * q^18 + 21230427174 * q^20 - 47057263940 * q^21 - 3442343910 * q^22 - 15842736534 * q^23 + 94553484290 * q^24 - 294640558020 * q^27 - 17774164556 * q^28 + 102726169530 * q^29 - 643189839240 * q^30 - 385043642942 * q^31 + 2378676720192 * q^33 + 158249007174 * q^34 + 408521183892 * q^35 + 1375134180422 * q^37 + 1543745804832 * q^38 + 603440813444 * q^39 - 8303553806742 * q^40 + 1443758220300 * q^41 - 4657636435362 * q^44 + 6106558559866 * q^45 + 9604057332832 * q^46 - 21302607302640 * q^47 + 25515630744334 * q^48 - 18255254395212 * q^50 + 19158460873088 * q^51 - 48159060495244 * q^52 - 78998282739512 * q^54 + 13393057779764 * q^55 + 137860752160332 * q^56 + 31257866131908 * q^57 - 69211880377042 * q^58 + 38643830633662 * q^61 + 238390785941076 * q^62 - 71567394446902 * q^63 - 498262566925124 * q^64 + 178535375770548 * q^65 + 57983772499388 * q^67 + 261849713539554 * q^68 - 115652283503244 * q^69 - 44377197355566 * q^71 + 93677094320796 * q^72 + 405163878377696 * q^73 - 405068893451898 * q^74 + 225803653508132 * q^75 - 802546741257484 * q^78 - 155549526248110 * q^79 - 124920621818622 * q^80 - 1098726050204828 * q^81 - 575036459162320 * q^82 + 1901862557545176 * q^84 - 939038947054838 * q^85 + 1783857741230148 * q^86 + 1466099551935802 * q^88 - 1809234886116972 * q^89 - 156603181182342 * q^90 + 2736989931074496 * q^91 + 4441473764128152 * q^92 + 2349942705291804 * q^95 - 7961673687938290 * q^96 - 2718145106426904 * q^97 - 2118270343699824 * q^98 + 173739293641872 * q^99

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